Zorana Banković
email: zorana@die.upm.es

David Fraga
email: dfraga@die.upm.es

José M Moya

Juan Carlos Vallejo
email: jcvallejo@die.upm.es

Álvaro Araujo
email: araujo@die.upm.es

Pedro Malagón
email: malagon@die.upm.es

Juan-Mariano Goyeneche
email: goyeneche@die.upm.es

Daniel Villanueva
email: danielvg@die.upm.es

Elena Romero

Javier Blesa
email: jblesa@die.upm.es

Juan-Mariano De Goyeneche

Detecting and Confining Sybil Attack in Wireless Sensor Networks Based on Reputation Systems Coupled with Self-organizing Maps

Keywords: wireless sensor networks, reputation system, self-organizing maps, outlier detection

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

WSNs consist of a large number of sensor nodes (also called motes). These nodes have to be very cheap, so they exhibit very limited power and computational resources, small memory size and low bandwidth usage and usually no tamperresistant hardware is incorporated with any of them.

The most aggressive and the most evasive of all the attacks on sensor networks is the Sybil attack [START_REF] Newsome | The Sybil Attack in Sensor Networks: Analysis & Defenses[END_REF]. In essence, it refers to the scenario when one (or more) node(s) claim to have multiple identities, either fabricated or stolen ones. In this way it is able to affect on various aspects on network functioning, some of them being routing protocols, voting (in trust schemes), fair resource allocation, etc. Thus, it is of highest importance to efficiently detect and confine this attack. Malagón, Juan-Mariano de Goyeneche, Daniel Villanueva, Elena Romero, Javier Blesa

We believe that spatial and temporal characterization of the data coming from the sensors can be of great importance in discovering manipulated data and/or compromised nodes. Any major data inconsistence can be connected to malicious data manipulation.

In this work we propose to detect presence the of the Sybil attack using a selforganizing map (SOM) algorithm for detecting data outliers. The first step in deploying any machine learning technique is to define the model of data. The model consists of certain number of characteristics, i.e. features, that describe all possible aspects of the phenomenon. Furthermore, in our case it is essential to be able to distinguish normal from anomalous behavior.

For that reason, we deploy temporal and spatial models of the sensors using ngrams. The temporal model is defined for each sensor, while spatial model considers groups of close sensors. Each n-gram in the temporal model consists of a predefined number of successive sensor values, while an n-gram in the spatial model consists of outputs of all the sensors that make the group. Therefore, the features are the n-grams and the feature values are the number of occurrences or the frequency of the corresponding n-gram during a certain period of time. Considering that number of ngrams is not constant within consecutive periods of time, SOM deploys methods for measuring distance between sequences presented in [START_REF] Rieck | Linear Time Computation of Similarity for Sequential Data[END_REF].

We further propose to couple the system of detection agents based on SOM with a reputation system. In our proposal, the output of an agent affects on the reputation system in the way that it assigns lower reputation to the nodes where it detects adversarial activities and vice versa. We envision a reputation system where every node is being examined by at least one agent that resides on a node in its vicinity and listens to its communication in a promiscuous manner, and executes one of the algorithms for detecting attacks or temporal and spatial inconsistencies. We further advocate avoiding any contact with the nodes that have low reputation (below certain threshold). In this way, the compromised nodes remain isolated from the network and have no role in its further functioning. Comparing to our previous work on the subject [START_REF] Moya | Improving Security for SCADA Sensor Networks with Reputation Systems and Self-Organizing Maps[END_REF][START_REF] Banković | Distributed Intrusion Detection System for WSNs based on a Reputation System coupled with Kernel Self-Organizing Maps[END_REF], in this work we propose improved way of calculating reputation based on the output of the SOM algorithm, which is more flexible and discriminative when it comes to distinguishing attacks from normal behavior. Furthermore, we present more thorough results on the behavior of the SOM algorithm in different scenarios.

The rest of the work is organized as follows. Section 2 present common solutions for treating the problem of the Sybil. Section 3 details the proposed solution, while Section 4 presents obtained results. Finally, conclusions are drawn in Section 5.

Previous Work on Coping with the Sybil Attack

The proposed solutions to the Sybil attack include [START_REF] Newsome | The Sybil Attack in Sensor Networks: Analysis & Defenses[END_REF]: 1. Radio resource testing which relies on the assumption that each physical device has only one radio; 2. Random key pre-distribution which associates the identity of the node to the keys assigned to it and validate the keys to see if the node is really who it claims to be; 3. Registration of the node identities at a central base station; 4. Position verification which makes the assumption that the sensor network topology is static. Each of the above solutions has its own drawbacks. For example, we do not know in advance that every physical device is going to have only one radio interface. Moreover, some of the MAC protocols rely on the fact that each node has more than one radio interface. The key pre-distribution is challenging, since attackers can deploy side-channel attacks in order to discover secret keys [START_REF] Bar El | Introduction to Side Channel Attacks[END_REF]. Finally, the last solution is applicable only in static networks, which is very uncommon scenario since there is often a number of mobile nodes that change their position.

Proposed Solution

Feature Extraction and Formation of Model

As previously mentioned our idea is to find temporal and/or spatial inconsistence in sensed data in order to detect manipulated data and/or compromised nodes. For this reason, we follow the idea presented in our previous work [START_REF] Moya | Improving Security for SCADA Sensor Networks with Reputation Systems and Self-Organizing Maps[END_REF] based on extracted ngrams and their frequencies within different time windows. For the purpose of illustration, we will give a short example for a sensor that detects presence. Let the sensor give the following output during the time window of size 20: 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0. If we fix the n-gram size on 3, we extract all the sequences of size 3 each time moving one position forward. In this way we can observe the following sequences and the number of their occurrences within the time window: 111 -occurs 6 times, 110 -2, 100 -2, 000 -6, 001 -1, 011 -1. Thus, we can assign them the following sequences: 111 -0.33, 110 -0.11, 100 -0.11, 000 -0.33, 001 -0.05, 011 -0.05. In our model, the sequences are the features and their frequencies are the corresponding feature values. Thus, the sum of the feature values is always equal to 1. In our algorithm this characterization is performed in predefined moments of time and takes the established amount of previous data, e.g. we can perform the characterization after every 40 time periods based on previous 40 values.

In a similar fashion, we form features for spatial characterization. The first step is to establish vicinities of nodes that historically have been giving consistent information. Furthermore, since an agent is supposed to reside on a node, vicinities are established using the nodes which information can reach the agent. In this way, an n-gram for spatial characterization in a moment of time is made of the sensor outputs from that very moment. For example, if sensors S1, S2, S3 each give the following output: 1 1 1 0 during four time epochs, we characterize them with the following set of n-grams (each n-gram contains at the first position the value of S1, the value of S2 at the second and the value of S3 at the third at a certain time epoch): 111 -occurs 3 times, 000 -occurs once, thus the feature value of each n-gram is: 111 -0.75, 000 -0.25, i.e. the frequencies within the observed period of time.

Detection of Sybil

The achievement of our design is based on the following two important assumptions: 1. The adversary can capture only a limited number of nodes, which means that most of the output data produced by the sensor nodes is normal. If this is not the case, it means that the adversary has become very powerful, so he is able to subvert any protocol in the network, which would require for the network re-initialization. 2. Output data produced under the influence of an adversary are statistically different from the output produced during the normal operation of the network. For this reason, we establish the detection of anomalies in data as outlier detection (an outlier is an observation that lies an "abnormal" distance from other values in a random sample from a population, i.e. extreme points in the data cloud). If any of these assumptions is not fulfilled, our model is not able to work properly.

We treat attacks as data outliers and deploy SOM explained in more detail in our previous works [START_REF] Banković | Distributed Intrusion Detection System for WSNs based on a Reputation System coupled with Kernel Self-Organizing Maps[END_REF]. There are two possible approaches for detecting outliers [START_REF] Muñoz | Self-Organizing Maps for Outlier Detection[END_REF] using clustering techniques depending on the following two possibilities: detecting outlying clusters or detecting outlying data that belong to non-outlying clusters. For the first case, we calculate the average distance of each node to the rest of the nodes (or its closest neighborhood) (MD). In the latter case, we calculate quantization error (QE) of each input as the distance from its group center.

In our case, due to the definition of features and the deployed distance function, the distance can take values from the range [0, 2]. The process of updating cluster centers results in the centers that have all the n-grams that appear in the elements that belong to them, and the sum of their values is 1. Thus, in the normal case, QE will have values between 0 and 1. However, if an adversary manipulates data, it will result in different n-grams, so the corresponding distance will be between 1 and 2. For the same reason, if we have anomalous data in the training, they will form their own clusters. In this case, MD will be between 1 and 2, which is taken as anomalous.

Recovery from Sybil

Every sensor node is being examined by agents that execute SOM algorithm and reside on nodes in its vicinity and listen to its communication. The agents are trained separately. The system of agents is coupled with a reputation system where each node has its reputation value that basically reflects the level of confidence that others have in it based on its previous behavior. In our proposal, the output of an agent affects on the reputation system in the way that it assigns lower reputation to the nodes where it detects abnormal activities and vice versa. We further advocate avoiding any kind of interaction with the low-reputation nodes: to discard any data or request coming from these nodes or to avoid taking them as a routing hop. In this way, compromised nodes remain isolated from the network and have no role in its further performance. After this, additional actions can be performed by the base station, e.g. it can revoke the keys from the compromised nodes, reprogram them, etc.

In this work the reputation is calculated in the following way. We define two reputation values, repQE and repMD based on the previously defined QE and MD values and afterwards joint reputation rep used for updating overall reputation based on these two values:

if (QE<1) repQE = 1;
if (MD<1) repMD = 1; else repQE=1-QE/2; else repMD=1-MD/2;

For the reasons explained in the previous chapter, the value (rep) for updating overall reputation is calculated in the following way:

if (QE>1)rep=repQE; else rep=repMD;

There are two functions for updating the overall reputation of the node, depending on whether the current reputation is below or above the established threshold that distinguishes normal and anomalous behavior. If the current reputation is above the threshold and the node starts behaving suspiciously, its reputation will fall quickly. On the other hand, if the reputation is lower than the established threshold, and the node starts behaving properly, it will need to behave properly for some time until it reaches the threshold. In order to achieve this, we use the function x+log (1.2*x) because it provides what we want to accomplish: if x is higher than 0.5, the output rises quickly, so the reputation rises; if x is around 0.5, the output is around 0, so the reputation will not change its value significantly; if x is smaller than 0.4, the output falls below 0. Finally, the reputation is updated in the following way:

if (last_reputation[node]>threshold) new_reputation[node]=last_reputation[node]+rep+log(1.2*rep); else new_reputation[node]=last_reputation[node]+0.05*(rep+log(1.2*rep));
If the final value falls out from the [0, 1] range, it is rounded to 0 if it is lower than 0 or to 1 in the opposite case. In this way, we achieve that once a node start behaving suspiciously, its reputation will fall quickly. Yet, if a malicious node starts behaving properly, it will have to maintain its correct behavior during some time in order to "redeem" itself.

However, if during the testing of temporal coherence, we get normal data different from those that the clustering algorithms saw during the training, it is possible to get high QE value as well. On the other hand, the spatial coherence should not detect any anomalies. Thus, the final reputation will fall only if both spatial and temporal algorithms detect anomalies. In the opposite case, its reputation will not change significantly. This is implemented in the following way:

if (value_rep < threshold) { if ( space_rep < threshold ) result = value_rep; else result = 1 -value_rep; } else result = value_rep;
where value_rep is the reputation assigned by the SOM for temporal characterization and space_rep is the reputation assigned by the SOM for spatial characterization.

Results

The proposed algorithm has been tested on a simulator of sensor networks developed by our research group. The simulated sensor network contains 200 sensor nodes that can take one of the possible 2000 positions. The network simulates a sensor network for detecting presence in the area of application, i.e. sensors give output 1 if they detect presence of a person or an object, or 0 if they do not detect any presence. The groups for spatial SOM algorithm are formed in a way that close sensors that should give the same output are placed in the same group. The simulation was carried out on a general purpose computer.

In our experiments the Sybil attack impersonates 10 existing sensor IDs. The duration of the experiment is 1000 time ticks. In the following we will present results in different scenarios regarding the presence of Sybil in training data and regarding two different definitions of MD value. In the first case, MD is defined as the medium distance to the three closest groups, while in the second case MD is the maximum of the three closest groups. This can be expressed mathematically in the following way:

Case 1:

( ) ( ) ( ) ( ) 2
i i i i i i i i i MD i i i i i i i ≠ ≠ - = ≠ - = - = - = ∑ = i i i i m x v m x v m x v m x v x (1)
Case 2:

( ) { } ( ) ( ) ( )
i i i i i i i i i i i i i MD i i i i ≠ ≠ - = ≠ - = - = ∈ - = i i i i m x v m x v m x v m x v x (2)
where v(x) is the centre to which the current input belongs.

Fig. 1.a and 1.b show the evolution of the reputation of every node after and before introducing the Sybil attack where the training stops at 600 th time tick and Sybil starts at 650 th . The MD value in the first case is calculated according to the formula (1), while in the latter case it is calculated according the formula (2). In both Fig. 2.a and 2.b we can observe a thick dark line, which stands for the group of nodes attacked by Sybil. (Sybil attacks random nodes in each simulation, which is the reason why the dark lines are at different position.) The dark color reflects their low reputation. Fig. 2.a and 2.b confirm that in both cases all the attacked nodes have been detected (Fake Positive line). However, in Case 2 higher number of nodes should be sacrificed in order to confine the attack (Fake negative line). This can also be concluded from Fig. 1.a and 1.b. However, the advantage of Case 2 is its robustness, which will be demonstrated in the following. In the following experiment Sybil starts at time tick 300. In the Case 2, the detector identifies and confines all the malicious nodes without having to change any of the parameters from the previous case (Fig. 4), while in Case 1 the detector detects the presence of the attack, but it is not able to confine it completely (Fig. 3). Experimenting with various parameters, we concluded that the maximum point to stop the training is 350 in order to completely confine the attack (Fig. 5). It is obvious that Case 1 is more sensitive to the presence of outlying data as minority, while Case 2 is more robust. These experiments also demonstrate that our system functions properly without the limitation of having (or not having) traces of attack in training data. Furthermore, we have demonstrated that detection possibilities of detectors can be enhanced through parameter changing. Concerning the time of detection and confinement of the Sybil, our system is capable of detecting and completely confining the attack if up to 30% of the existing IDs have been taken by the Sybil. The presence of the attack is detected at the end of the first testing cycle in all the cases, while the confinement time spans from one to four testing cycles and becomes higher as the Sybil takes more than 15% of the IDs.

Conclusions

In this work we have presented a novel approach for coping with the Sybil attack in wireless sensor networks. We have proposed unsupervised machine learning SOM algorithm for detecting outliers in data and deploys a feature set that is more general than those presented by the solutions of the state-of-the-art. Furthermore, it does not depend on the presence (or non-presence) of anomalous data during the training.

The idea of confining the Sybil is based on assigning reputation values to the nodes according to the decision of SOM algorithm. In this way, malicious nodes become isolated from the network which will impede them to further propagate their malicious activity. Our experiments demonstrate that our system is capable of detecting and confining Sybil attack.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Reputation Evolution (a) Case 1 (b) Case 2 Fig. 2.a and 2.b show the detection evolution in both of the cases. In these figures real positives are well-behaved nodes, real negatives are the ill-behaved nodes. Fake positives are non-detected ill-behaved nodes, while fake negatives represent the portion of well-behaved nodes falsely detected as ill-behaved.In both Fig.2.a and 2.b we can observe a thick dark line, which stands for the group of nodes attacked by Sybil. (Sybil attacks random nodes in each simulation, which is the reason why the dark lines are at different position.) The dark color reflects their low reputation. Fig.2.a and 2.b confirm that in both cases all the attacked nodes have been detected (Fake Positive line). However, in Case 2 higher number of nodes should be sacrificed in order to confine the attack (Fake negative

Fig. 2 .

 2 Fig. 2. Detection Evolution (a) Case 1 (b) Case 2

Fig. 3 .

 3 Fig. 3. Case 1 (a) Reputation Evolution (b) Detection Evolution

Fig. 4 .Fig. 5 .

 45 Fig. 4. Case 2 (a) Reputation Evolution (b) Detection Evolution


Tomislav Stipancic
email: tomislav.stipancic@fsb.hr

Bojan Jerbic
email: bojan.jerbic@fsb.hr

Self -adaptive Vision System

Keywords: active vision system, self adaptation, active behavioral scheme, experiment planning, response surface methodology

Light conditions represent an important part of every vision application. This paper describes one active behavioral scheme of one particular active vision system. This behavioral scheme enables an active system to adapt to current environmental conditions by constantly validating the amount of the reflected light using luminance meter and dynamically changed significant vision parameters. The purpose of the experiment was to determine the connections between light conditions and inner vision parameters. As a part of the experiment, Response Surface Methodology (RSM) was used to predict values of vision parameters with respect to luminance input values. RSM was used to approximate an unknown function for which only few values were computed. The main output validation system parameter is called Match Score. Match Score indicates how well the found object matches the learned model. All obtained data are stored in the local database. By timely applying new parameters predicted by the RSM, the vision application works in a stabile and robust manner.

Introduction

The development of robotics is dictated by increasing demands of humanity. Today's robots are involved in almost all areas of human activity, namely: medicine, technology, research and accessibility of hazardous or unclean areas, etc. Service Robotic is a term that appears to indicate just one step in robot evolution. This evolution moves from the simplest industrial robots and goes to the highly sophisticated personal robots, which aim to be universal. Such robots would be able to exist alone in the surroundings just like human beings, regardless of their original purposes. The prerequisite for intelligent behavior of any artificial system is thus the ability to perceive its environment [START_REF] Stipancic | Robust autonomous assembly in environment with relatively high level of uncertainty[END_REF]. To do that, it is necessary to establish some kind of active sensing structure which is able to deliver timely fresh information to the system. Such a structure has to have the capability to determine what to do with the acquired information and to make proper decisions with respect to timely appropriate actions. Information detection and determining what to do with the collected information in a controlled manner is an approach in robotics called Active Sensing [START_REF] Chen | Active Sensor Planning for Multiview Vision Tasks[END_REF]. Such systems can often contain different subsystems responsible for different behavioral schemes. There are trends in today's robotics which are suggesting that robotic systems have to include the active sensing unit with one or more active behavioral schemes. Active Sensing Unit has to decide what behavioral scheme to choose according to an actual environmental savior or actual system needs and to seek optimal solutions to make desired actions. For example, Active Placement Scheme can be related to the vision sensor positioning, Active Vision Parameter Scheme can be related to the proper vision parameter determination, Active Calibration Scheme can be related to the timely calibration of vision sensors, Active Model Construction Scheme can be related to the 3D object interpretation, Active Illumination Scheme can be used for choosing proper light sources at the right moment, etc. [START_REF] Chen | Active Sensor Planning for Multiview Vision Tasks[END_REF]. In the proposed approach it is very easy to find similarities with human beings because they cannot imagine their life without the system of active perception. Humans collect new information with their vision sensors -eyes. The brain is constantly analyzing and triangulating its 3D environment combining collected information with previously collected experience and knowledge, defining distances and relationships between objects in the observed scene. Active eyes usage goes to such lengths that people sometimes automatically change the viewing angle and object distances in order to complement missing information.

This article describes one behavioral scheme as a part of the research related to the Active Sensing. The main task of this particular behavioral scheme is to take care of the active vision parameter adaptation and it will be the part of the robotic system which conducts two more schemes: Active Calibration Scheme and Active Positioning Scheme. Active Vision Parameter Adaptation Scheme provides the needed vision acquisition accuracy and decreases the level of noise which can occur in constantly changing environmental conditions. High accuracy and low level of noise are very important for robotic vision, especially in assembly or disassembly operations where robots have to precisely manipulate with small parts, often in poor light conditions. The proposed scheme decreases the need for special light sources and techniques which are the most common vision application ingredients. The main accent was set on an experiment planning by using Response Surface Methodology (RSM) to develop Active Vision Parameter Adaptation Scheme. RSM [START_REF] Box | The exploration and exploitation of response surfaces: some general considerations and examples[END_REF] was used to determine the connection between input and output parameters at the beginning. Luminance in the room was used as an input parameter value. Intrinsic vision sensor parameters, such as Brightness and Gain, were used as an output value. Great potential lies in experiment planning [START_REF] Stipancic | Substantial vision application settings analysis[END_REF]. In order to have optimal application output results it is very important to see a picture large enough at the beginning. Such an approach enables us to have better understanding of parameters dependences and gives the opportunity to guide the experiment to produce better results at the end. The presented scheme can be also used as a framework for other applications, because almost all vision sensors have similar or the same input vision sensor parameters. Along with such a conclusion, the analyzed idea was presented like a framework in order to facilitate easier future reproduction of the concept for everyone.

Contribution to Technological Innovation

Traditional methods for machine vision to better interpret scenes are usually focused on post-image processing. Usually, these approaches deal with current states to extract more information about the object surfaces AFTER vision sensor taking the pictures. Approach proposed in this paper is focused on adaptation of the vision system to the current light conditions BEFORE vision sensor taking the pictures. Such an approach facilitates further vision analysis and saves time-consuming enhancement processing, which is very important in a machine vision system, especially for realtime applications [START_REF] Chen | Active Sensor Planning for Multiview Vision Tasks[END_REF].

Equipment and Software

A Basler scA1400-17fc camera was used to acquire images from the object in the scene. The main characteristics of this camera are relatively high resolution (1392 × 1040 px) and color image representation. It is rather small and suitable for mounting directly to the robot hand. In this application, the camera was connected with the NI Compact Vision System (NI CVS -1456) which was used for image acquisition and later image processing. The CVS is an all-in-one vision system which comes from National Instruments Company and contains a processor, a memory, an operating system and an I/O interface. The vision application set-up was carried out by means of the NI Vision Builder for Automated Inspection (VBAI) software, based on NI LabView and containing a number of tools for image acquisition, image preprocessing and processing, system communication with other external devices, etc. This software has to be installed on a PC. After the application configuration, the next step was to upload all data from the PC into the CVS, responsible for all later actions regarding the vision application. Fig. 1 shows the equipment and the hardware system configuration used in the experiment. The device for measuring the luminance is called a luminance meter. In this application the XYL-III All Digital Luminance-meter was used. To provide measurements and later data analysis this device can be connected to a PC via RS-232 interface. Luminance describes the amount of light leaving a surface in a particular direction and can be thought of as the measured brightness of the surface as seen by the eye or a vision sensor and it is very important for this particular application [START_REF] Inanici | Evaluation of high dynamic range photography as a luminance data acquisition system[END_REF]. It is expressed in Candelas per square foot, or more commonly, Candelas per square meter (Cd/m 2 ).

Experiment Description

Reliability of scene inspection by a vision system is strongly connected to the set of parameters chosen for a specific vision application [START_REF] Stipancic | Robust autonomous assembly in environment with relatively high level of uncertainty[END_REF]. If environmental conditions change over time, these parameters should either be optimized at the beginning of the process or changed on-line constantly. By changing vision parameters on-line constantly, vision system attains fresh information during the time which results with relatively high robustness and precision. The first step of the Active Vision Parameter Adaptation Scheme development was to make an experiment which was crucial for dependence determination of inner parameters. Beside that, the experiment brings hidden information on the system response regarding different input values. Such information can help in determining weak points of the experiment enabling better process understanding and optimization. The relationship between input and output factors was provided by means of Response Surface Methodology (RSM). The RSM [START_REF] Myers | Response surface methodology: process and product optimization using designed experiments[END_REF] can be found as a part of the Design Expert software [START_REF]Users Guide: Multifactor RSM & General One-Factor[END_REF] which was used in this particular case and it represents a collection of mathematical and statistical techniques used for process optimization and analysis. It consists of a group of techniques that can be used in the empirical study of relationships between one or more measured responses with an arbitrary number of input factors. It comprises: designing a set of experiments, determining a mathematical model and the optimal value of the response, thus providing a better understanding of the overall system behavior. The empirical relationship is frequently obtained by fitting polynomial models. The main purpose of the first and the second order experiment designs was data collection for fitting such models. The first order polynomial model can be expressed by the general Equation 1,

∑ = + + = k j j j x y 1 0 ε β β (1)
where y is response, β 0 , β 1 ,... β k are the unknown regression parameters, x 1 , x 2 ,… x k are the input factors, k is the number of input factors and ε is random error. The CCD (Central Composite Design) was used to describe responses and to estimate parameters in the model. This design consists of a factorial portion, an axial portion and a centre point. It's well suited for fitting a quadratic surface, which usually works well for the process optimization. If the distance from the center of the design space to a factorial point is ±1 unit for each factor (Table 1.), the distance from the center of the design space to a star point is ±α with |α| > 1. The precise value of α depends on certain properties chosen for the design and on the number of factors involved.

Applied load and sliding distance were considered as model variables. So, with respect to the system input parameters (Luminance and Match Score), the system will use output factors (Gain and Brightness) previously predicted by means of the RSM. A particular vision tool called Match Color Pattern Vision Tool (Fig. 2.) was used to detect an object in the field of view. This tool can be found as a part of the vision software (VBAI). In the beginning of the configuration, the tool has to learn a template which contains an object(s) or a feature(s) of interest in the first line. Later, with respect to the learned template, the vision tool searches for similarities in the field of view. The match score is a value that indicates how similar a potential match is to the template image and it ranges from 0 to 1000. A score of 1000 indicates the perfect match. It was determined that a value lower then 800 of the match score results with positioning error which was too large for the developed vision application. Such values were not taken into consideration. The presented method can be used in combination with different vision tools for different purposes. During the experiment, a luminance value ranged between 0 and 300 cd/m 2 . The experiment was made far from windows. This resulted with relatively stabile light conditions without high values of sunlight illumination. To provide even more stabile conditions, windows were covered with curtains. It was very important to repeat the experiment in different light conditions to analyze as many possibilities as possible which resulted in a more robust application. A luminance measurement was taken with and without curtains on windows and neon lights switched on and off. A gain value represents the number of times a vision device amplifies a light input. It can be very useful in poor light conditions where it is necessary to make a more visible scene. Gain values ranged between 192 and 1023. An image brightness definition was connected with a pixel definition and it ranged between 0 and 255.

The Design-Expert software was used for the experiment design and analysis. The Design-Expert contains a set of statistical and numerical tools that can be used for processes optimizations, predictions, etc. The first step of the experiment design was to enter information about the Central Composite Design -CCD (Alpha Level, Center Points, etc.) and information about the analyzed vision application (Table 1). The software led us to define a missing portion of the CCD. By entering the data, the Design-Expert calculates the coded distance "alpha" for placement on the star points. The next step was to make a real experiment by combining data provided by the Design-Expert and to acquire responses. For the purposes of this experiment, 13 input factor variations (Figure 4) were collected and analyzed. By filling values into the table, process of designing the experiment was completed. As it was mentioned before, the Design-Expert has a broad set of numerical and statistical tools for extracting extended information about the analyzed process. In this paper the main emphasis was set on the process prediction. Figure 5 shows the Point Prediction Table which holds information about input factor combinations and their related responses.

Vision Application Description

The Active Vision Parameter Adaptation Scheme described in this article contains: a vision application (NI Compact Vision System -software and hardware), a PC, a luminance meter and a database. The PC was used as a host of the Active Behavioral Unit and the vision software (VBAI). The main task of the Active Behavioral Unit was to provide communication and data management between all system components. It is a fact that the vision sensor takes pictures of the object from different angles and positions in the space. That results in timely different light conditions between picture shots. To ensure relatively similar conditions for taking pictures from different positions, the vision system gets new vision parameters from the database before taking new pictures. Information acquired from the luminance meter was the main criteria for determining which parameters to pick from the database. Figure 6 shows the active sensing flowchart which describes one common "pick-and-place" robot application.

Conclusion

This paper provides a description of a particular Active Behavioral Scheme which is included in one bigger robotic system that relies on the Active Sensing paradigm. Described scheme enables the system to become much more robust and to become relatively resistant to timely new light conditions in the observed scene. The vision parameters determination is provided by means of Response Surface Methodology which can also be used for an experiment weak point determination. Instead of using the RSM, future work will be related to usage of neural networks in connections between input and output parameters determination. It would be interesting to analyze influence of other factors to vision application too (such as measuring of the room ambient light). The research described in this article will be a part of a PhD Thesis where the main emphasis will be set on Active Placement Scheme which is taking care of spatial positioning of the Vision Sensor [START_REF] Curkovic | Hybridization of adaptive genetic algorithm and ART 1 neural architecture for efficient path planning of a mobile robot[END_REF].

Fig. 1

 1 Fig. 1 Equipment and hardware system configuration.

Fig. 2

 2 Fig. 2 Match Pattern Color Vision Tool setup.

Fig. 3

 3 Fig. 3 Design -Expert Layout Table.

Fig. 4

 4 Fig. 4 Design -Expert Layout Table along with Factors Tool Window. Input factor values can be changed by means of the Factor Tool Window. It is sufficient to move the slider placed at the Factors Tool Window to see new responses with respect to the input values. The Design -Expert Layout Table provides information used for future point prediction optimizations of this application. The next configuration step was related to the data storage into the database.

Fig. 5

 5 Fig. 5 Active Sensing flowchart.

Table 1

 1 Factors for response surface study.

	Factor	Unit	Low Level (-1)	High Level (+1)
	Luminance	Cd / m 2	0	300
	Match Score	-	800	1000


Paulo Barbosa

Franklin Ramalho
email: franklin@dsc.ufcg.edu.br

Jorge Figueiredo

Anikó Costa

Luís Gomes

Antônio Junior

Semantic Equations for Formal Models in the Model-Driven Architecture

Keywords: Model-Driven Architecture, Petri nets, Denotational Semantics, Transformations, Semantic Equations

Semantic equations are important pieces of the denotational semantics approach that enable the translation of syntactic constructs of models to semantic domains. In a previous work, we have extended the Model-Driven Architecture (MDA) four-layer proposal of architecture in order to incorporate formal semantics to its artifacts. Thus, semantic equations are key elements in this extended architecture. In this paper, we propose an approach to incorporate semantic equations described by model transformations in the MDA infrastructure. As a result, we automatically generate semantic models from the syntactic models involved in the MDA transformations. Therefore, the semantic equations play an important role in the MDA architecture since they allow the construction of tools for automated reasoning for several purposes, such as: (i) verification of semantics preservation in model transformations; (ii) choice of the best format to represent meaning and behavior of models and (iii) automatic generation and production of quality compilers. For instance, we claim that in the scenario of model transformations involving concurrent models described using Petri nets, semantic concepts can be more easily and appropriately handled in the MDA architecture. We have evaluated our approach by applying semantic equations to Petri nets models in a project for embedded systems codesign.

Introduction

In the Model-Driven Architecture (MDA) [START_REF] Miller | MDA Guide Version 1.0.1[END_REF] [2], a model is an abstract or concrete representation of a domain. They are described by metamodels that express the elements of the language. Model transformations process these elements through a set of definition rules that describe how to generate an output model from an input model. Although MDA promises to overcome important gaps in the software engineering, it has not specified ways to ensure that its artifacts are correctly represented. Particularly, the lack of a formal representation of the involved models in the four-layer MDA architecture leads to undesirable situations of ambiguity and low reliability.

In [START_REF] Barbosa | An Extended MDA Architecture for Ensuring Semantics-Preserving Transformations[END_REF], we have proposed an extension of the four-layer MDA architecture in order to incorporate formal semantics in its infrastructure. We introduced semantic metamodels and models, and other artifacts to verify semantics equivalence between the input and output models involved in MDA transformations and to prove properties about them. This proposal was evaluated in the concurrent systems domains, through models represented using Petri nets [START_REF] Girault | Petri Nets for Systems Engineering[END_REF] in a project of embedded systems co-design [START_REF] Gomes | Formal Methods for Embedded Systems Co-design: the FORDESIGN Project[END_REF].

Assuming the importance of formal semantics in the modeling domain, to apply it to a model it is necessary the assignment of meanings to its sentences or components.

This needs to be treated in the proposal of the extension of the MDA architecture. This assignment should be given by a mathematical model that represents every possible computation in the language that describes the model. It is expected with the semantic description of a model the following benefits: (i) the development of partial evaluation techniques for interpreting and compiling models in the MDA architecture; (ii) the automatic generation of compiler semantics definitions; (iii) a foundation for understanding and evaluating the design issues; and (iv) a valuable reference for transformations that involve this model. In this sense, the formal definition is necessary to guarantee the preservation of properties in the output model after a transformation, which is the main goal of a PhD thesis that guides this work.

The denotational semantics [START_REF] Scott | Towards a Mathematical Semantics for Computer Languages[END_REF] is one of the most employed approaches to provide formal semantics. It is specially addressed for the case in which the necessity of constructing mathematical objects to represent meaning of models emerges, as is in this work. In this approach, the meaning is given by functions that map syntactic elements to mathematically well-defined sets. This mapping is usually named as semantic equations.

Although semantic models are considered as important pieces for a formal architecture, in the extension of the MDA architecture they make sense only in the case of being automatically generated from the syntax. Most approaches based on semantic models depend on the expertise of a domain engineer, demanding costs, low reliability and very imprecise specifications as representations of what of most precise a model should have [START_REF] Hausmann | Dynamic Meta Modeling: A Semantics Description Technique for Visual Modeling Techniques[END_REF].

In this paper, we claim that the extraction of semantic models in MDA must be responsibility of the semantic equations, following declarative formal rules using automated tools according to the MDA standards. Semantic models can be described by a metamodel with the same expressive power as the metalanguage of denotational semantics. This fills the necessity of compiler generators guided by semantics as a unified framework. Denotational semantics specifications may have the format of a MDA transformation, providing this unification as mathematical objects and turning modeling languages closer to this metalanguage of formal semantics.

The structure of this paper is as follows. Section 2 discusses how this work can contribute to innovation in the specific MDA technology. Section 3 and 4 presents the main background issues necessary for understanding this work, namely our previous proposal of the extending the MDA architecture and the denotational semantics concepts involved. Section 5 gives details about our proposed approach to specify semantic equations illustrating and evaluating for specific models. Section 6 discusses related works. Finally, Section 7 discusses about the benefits and possible drawbacks of the presented work, and the final remarks.

Contribution to Technological Innovation

In this work, we propose and discuss an approach to introduce semantic equations as formal specifications in the MDA architecture. Considering MDA transformations as the pivotal element to specify semantic equations, some issues emerge to be answered, as pragmatic aspects of the transformation language and some theoretical aspects related to computability. These issues are addressed and discussed in this work.

We evaluate this proposal with a well-established and appropriate extraction from the syntactic constructs to semantic domains in the concurrent domain with Petri nets models. This allowed the verification of semantics preserving transformations as well as an on-the-fly occurrence graph generation system for it. Moreover, with the proposal of a representation to semantic equations, semantic properties of models can be checked for several purposes.

The Extended MDA Four-Layer Architecture

The current MDA architecture, shown in Figure 1, consists of four layers: (i) M0 involves executable representations of models as code; (ii) M1 describes the concrete syntax representation of a given model; (iii) M2 provides the metamodel which serves as a grammar to describe the model syntax developed at the layer M1; and (iii) M3 describes the layer M2 by using MOF, the Meta-Object Facility [START_REF]OMG: Object Management Group[END_REF]. Since MOF describes itself, it is not required further metamodels. The model transformations are able to automatically generate output models from input models at the layer M1. They are defined in terms of metamodel descriptions and cope only with syntactic/structural aspects.

Our proposal of an extended MDA architecture for incorporating formal semantics is shown in Figure 2 as gray modules at the layers M1 and M2. Semantic equations, which are the focus of this paper is highlighted and will be discussed. Briefly, the other new inserted parts are:

• Semantic metamodel, which defines (i) the state configuration of a model or a program according to the semantic specifications; and (ii) the dynamic semantics capturing the state infrastructure of language constructs as well as how they use or change an existing state. It serves as a concretization for theories of formal semantics. • Semantic model, which instantiates the state configuration metamodel. Since semantic metamodels represent theories of formal semantics, semantic models are representations according to these theories. • Simplification rules, which are able to perform the inference and computation of state configurations. They instantiate the dynamic semantics.

These rules are implemented according to the chosen computation mechanism. • Formal checker, which is complementary to the simplification rules, also instantiates the dynamic semantics, and it is required to prove properties about the equivalence of the verified input and output models. The role of semantic equations in this architecture is to define mappings, from the language's abstract syntax structures to meanings drawn from semantic models. They are illustrated as the small arrows from the syntactic models to the semantic models in the layer M1.

Fig. 2 The extended architecture to incorporate formal semantics.

Denotational Semantics for Petri nets

The main aim of denotational semantics is to provide a proper mathematical foundation for reasoning about programs and programming languages. It is based on a set of denotations, i.e., a function with arguments that represent expressions before and after executing. Denotations can inductively be defined by using any formal mapping to specify how the denotations of components are combined.

To give the denotational semantics of a language, a suitable collection of meanings is necessary. The most used theory is called Domain Theory, which employs structured sets, called domains, and their operations as data structures for semantics. These domains plus their operations constitute a semantic algebra. According to [START_REF] Schmidt | Denotational Semantics: a Methodology for Language Development[END_REF], the semantic algebra: (i) clearly states the structure of a domain and how its elements are used by the functions; (ii) modularizes and provides reuse of semantic definitions; and (iii) makes analysis easier.

We have chosen the Petri nets formalism as the description language of the involved models because this language is already well-accepted in the MDA community [START_REF] Hillah | Model Engineering on Petri nets for ISO/IEC 15909-2: API Framework for Petri Net types metamodels[END_REF] and has a good support to formal semantics. It was designed as a graphical and mathematical formalism for modeling concurrent systems. Moreover, this work is inserted in the context of a project that proposes the use of Petri nets for the co-design of embedded systems.

We take the nets analyzed in [START_REF] Barbosa | Checking Semantics Equivalence of MDA Transformations in Concurrent Systems[END_REF] which are shown in Figure 3 and refers to the model of a parking lot controller when considering a centralized implementation or a distributed implementation relying in two components (synchronized through transition firing) after applying the Splitting Operation. Fig. 3 Two nets that represent models before and after the Splitting Operation.

In [START_REF] Meseguer | Petri nets are Monoids: a new Algebraic Foundation for Net Theory[END_REF], Meséguer and Montanari use the category theory to claim that a Petri net model is to be translated to an ordinary, directed graph equipped with two algebraic operations. These operations correspond to the sequential and parallel composition of transitions (representing behavior), with a distributive law between these compositions.

The model has to provide the generators of the algebraic structure which the responsibility of the automatic mapping is given to the semantic equations.

The understanding of concurrency in terms of algebraic structures over graphs is very important for Petri nets modelers. It has the potential of unifying several views of semantics formalisms. Moreover, this structure can be manipulated by formal methods tools to be employed in several sorts of analysis and satisfying some requirements that are hard to solve by most editors and tools available for this domain. As an example, several formal tools could afford to the state space explosion problem, by providing an on-the-fly way of reasoning over occurrence graph structure of the Petri net model if it is seen as this algebraic structure.

By using more specific terms, this ordinary graph has a set of nodes as a commutative monoid S ⊕ generated by the set S of places and the empty marking as identity. The sum + of transitions represents the parallel firing of transitions, and the sequential firing of transitions is denoted by the operation. By the guarantee of the closure property, we are representing computations through simple transitions.

For example, we have that the next code fragment is a representation of the semantic model for the Maude System [START_REF] Clavel | Maude: Specification and programming in rewriting logic[END_REF] from the net before the Splitting Operation of Figure 3 as an illustration of the role that semantic models can play after extracted from the semantic equations. The Commutative operation + is present in line 7 with the specified properties. This semantic model may be used for several verification purposes, such as model-checking or theorem proving.

MDA Semantic Equations

In order to incorporate semantic equations into the extended MDA architecture, it is necessary to cope with pragmatic and formal issues. The former concerns requirements related to the language and tools that will represent semantic equations whereas the latter deals with theoretical aspects to ensure composition and recursion as is required by denotational semantics specifications.

Focusing on the pragmatic issues, there are three requirements that must be observed on the language used to represent semantic equations: i.

It must be able to represent the functional characteristics of classical definitions for denotational semantics. Supporting the declarative paradigm allows pattern matching that is essential to describe functional operations. Moreover, this seems also necessary because the language that will describe the codomain of semantic equations as in denotational semantics is completely based on functional constructs, such as functions definitions and applications. ii.

It must support the representation of actual features of most programming models, representing aspects of programming and modeling languages. Concepts such as sequentiality, concurrency, non-determinism and an infrastructure to represent states are present whatever be the domain of the semantic equations application. iii.

It must manipulate and execute properly the semantic equations. This will enable the integration with other formal methods tools. A powerful toolset of the language to support this seems to be essential to our solution. On the other hand, there are two theoretical aspects of the language that must be addressed:

iv.

It must be fully (or partially) compositional. The understanding of composite expressions as transformations rules makes the proof of properties about semantics easier, allowing the translation of syntactic pieces to a semantic metalanguage represented as a semantic algebra metamodel. This represents a challenge but also a useful improvement because there are usually propositions, axioms and theorems that have been developed for this metalanguage. Finding such a compositional language allows us to reason using induction over the grammar of the modeling language, since this grammar can be described by metamodels. v.

It must allow recursion over the grammatical structure (i.e. the metamodel) of the language it interprets. In other terms, it must enable to extract the current state of the model in terms of a meaningful representation (i.e. the semantic model). This is made by carrying a structure representing the environment of a program or of a model. When the input model (i.e. syntactic model) is given to the engine, the transformation explores it at the top-level term, creating any necessary context into an environmental structure, passes this structure into a recursive call for each of the subterms, and provides the terms able to be analyzed based on what it gets back from the mapping that represents the semantic equations.

This work characterizes semantic equations as, essentially, MDA transformations. In order to prove this, we choose a transformation language and MDA standards to accomplish the presented pragmatic and formal issues. This was evaluated through a case study that we conducted for the mapping from syntactic structures to semantic domains. For this, we have chosen the ATL language [START_REF] Bezivin | The ATL Transformation-Based Model Management Framework[END_REF], because this language is able to satisfy the mentioned requirements. Moreover we discuss this justification by using Petri nets models.

Concerning the previously pragmatic addressed issues, we have a discussion about each topic. About (i), classical definitions of denotational semantics are present requiring a declarative approach for the definition of functional algebraic concepts. In (ii), we have that imperative fragments are necessary in when defining semantic equation, dealing with common concepts such as variables and sequencing. Finishing the first part of issues, we have that in (iii), ATL allows the manipulation of formal semantics concepts using an editor and an engine tool able to execute these specifications according to [START_REF] Bezivin | The ATL Transformation-Based Model Management Framework[END_REF]. Concerning the theoretical issues, we see that in (iv), the compositionality of ATL enables the definition of the mapping into simpler parts, treating each algebraic structure as mathematics does and combining these rules for the whole. Finally the issue is answered because ATL searches recursively in the language metamodel, dealing with the compositionality of the subterms, converting abstract syntax structures into the predefined algebraic structures responsible for the representation of meaning as semantic models.

Related Works

Regarding to related works we concentrate on the expected benefits of having semantic models using MDA standards through semantic equations. [START_REF] Hu | Mapping UML Diagrams to a Petri Net Notation for System Simulation[END_REF] proposes the use of Petri nets to simulate the behavior of models in MDA. The models are described in UML state chart Diagrams and then converted to a Colored Petri nets representation. In this case, Petri nets models act as semantic models. The work presented in [START_REF] Weisemller | Formal definition of mof 2.0 metamodel components and composition[END_REF] proposes the MOF formalization reusing the category theory modularization concepts from algebraic specification languages. This provides a graph-transformation-based formalization of MOF, upgrading MOF with new interfaces and a composition operator based on graph morphisms. It is the same idea reused here, however is a proposal for the meta-metalanguage of the MDA framework, and not for a specific domain as we made for Petri nets. In [START_REF] Kelsen | A lightweight approach for defining the formal semantics of a modeling language[END_REF] the authors propose a novel approach for the definition of a formal semantics to languages based on the Alloy language. It intends to turn semantics definitions easier, encouraging the adoption of formal techniques. This work advocates that its approach provides two main advantages: uniform notation and a mechanism for analysis. Finally, [START_REF] Arévalo | Building abstractions in class models: Formal concept analysis in a model-driven approach[END_REF] concentrates in some specific problems commonly found when using MDA such as refactorings and extraction of meanings of UML models. This work makes use of mathematical techniques, specially the lattices theory, to discover abstractions from a set of formal objects. This seems very useful for providing sound refactorings. The similarity with our work is that semantic equations can also be viewed as ATL transformations, when mapping a UML diagram to a formal context (the semantic model).

Final Remarks and Future Works

It is already known that MDA's artifacts and processes lack a semantic model, and that there is no way to ensure that its transformations preserve the semantics. The use of an underlying semantic model for verification purposes is a fundamental step in the MDA transformations, in order to have a formal definition of the involved artifacts in the transformation and be able to check its correctness by comparing whether the input and output models are consistent according to the semantic model definition.

Semantic models are also suitable for a compiler generation system for MDA. Currently, the models and metamodels built in this infrastructure can deal only with abstract and concrete syntax terms. Semantic equations are able to map to the denotational definition from a programming or modeling language. Concepts like semantic domains and semantic equations are specifications and the concrete implementation of a MDA compiler is encouraged. It enables dealing with semantic concepts such as scope, declarations, functions, type inference and type checking, control flow, exceptions and much more. Thus, the suitability of a semantic model is a promising step towards the automatic generation and production of quality compilers and processors.

We intend to analyze our approach in other scenarios than Petri nets modeling. Although each scenario have particular properties to be considered when providing semantic models by means of semantic equations, we advocate that our approach deserves special attention in all cases since: (i) the provided semantic metamodel may be reused; (ii) semantic models are required in any scenarios (iii) the pragmatic and theoretical issues raised in this work must be addressed.

Fig. 1 .

 1 Fig. 1. The current MDA Architecture.

Acknowledgments. This work was partially supported by the collaborative project Verificação Semântica em Transformações MDA Envolvendo Modelos de Redes de Petri (MDA-VERITAS -Semantic Verification in MDA Transformation using Petri nets models), funded by FCT -Fundação para a Ciência e a Tecnologia (Portugal) and CAPES -Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Brazil) (http://www.uninova.pt/~mda-veritas).


Lazaros Iliadis
email: liliadis@fmenr.duth.gr

Stergios Skopianos

Stavros Tachos

Stefanos Spartalis

A Fuzzy Inference System using Gaussian distribution curves for forest fire risk estimation

Keywords: Fuzzy algebra, Gaussian distribution curves, Fuzzy Inference System, wildfire risk

This paper describes the development of a fuzzy inference system under the MATLAB platform. The system uses three distinct Gaussian distribution fuzzy membership functions in order to estimate the partial and the overall risk indices due to wild fires in the southern part of Greece. The behavior of each curve has been investigated in order to determine which one fits better for the specific problem and for the specific areas. Regardless the characteristics of each function, the risky areas have been spotted from 1984 till 2007. The results have shown a reliable performance over time and they encourage its wider use in the near future.

Introduction

Every year, forest fires destroy important forest areas, with enormous consequences. The problem of forest fires occurs mainly in the Mediterranean countries, in Australia, in Canada and the United States [START_REF] Iliadis | A decision support system applying an integrated Fuzzy model for long -term forest fire risk estimation[END_REF]. Especially in Greece due to the lack of a proper cadastral survey, the problem of forest fires is related to political elections and also to the cycles of drought [START_REF] Kailidis | Forest fires. 3rd edition. Giahoudi-Giapouli editions[END_REF] [START_REF] Kailidis | The forest fire problem in Greece[END_REF]. More detailed analysis on the problem of forest fires in Greece can be found in [START_REF] Markalas | Forest fires in Greece in 1993[END_REF] [START_REF] Xanthopoulos | Greek forest fires and property damage: A brief history[END_REF] [START_REF] Xanthopoulos | Forest fires in Greece: Past, present and future[END_REF].

Fuzzy logic systems are quite flexible and they are used for several purposes such as modeling, forecasting and classification [START_REF] Iliadis | A computer-system that classifies the prefectures of Greece in forest fire risk zones using fuzzy sets[END_REF]. This research effort aims in the development of a fuzzy inference system, that estimates an integrated fuzzy forest fire risk index offering an overall view of the problem. This is achieved by employing three distinct fuzzy membership functions (of the same family) namely the Gaussian, the Sigmoid and the S-shaped one. The application of fuzzy logic enhances the ability to model proper linguistics that are used in the consequent part of the developed rule-based system. The application area concerns the Greek forest departments of Attica and Peloponnesus which are located in the southern part of the country. The whole research has been performed for the period 1984 to 2007 and the estimation of the integrated risk index has been achieved by considering the annual number of forest fire breakouts and the annual burned forest area for each forest department.

Literature Review

In order for the appropriate authorities to adopt efficient fire prevention and protection measures, the assistance of modern technology is required towards the evaluation of forest fire risk [START_REF] Iliadis | A decision support system applying an integrated Fuzzy model for long -term forest fire risk estimation[END_REF][8] [START_REF] Lin | The Development, Systems, and Evaluation of Forest Fire Danger Rating: A Review[END_REF]. Deeming et al [START_REF] Deeming | The National Fire Danger Rating Sstem USDA[END_REF], developed the national fire danger rating system (NFDRS), which is still used in the USA after some improvements. It is a system that produces the daily ignition component index and also the man caused risk index. There have been many studies in the United States, in Australia, in New Zealand and in Europe for the long term evaluation of fire risk. A system that evaluates daily as well as long term fire danger is EFFIS (European Forest Fire Information System). It has been developed by the Institute for Environmental and Sustainability Land Management which resides in Italy [START_REF] Ayanz | The European Forest Fire Information System (EFFIS)[END_REF]. In reality EFFIS is an attempt towards the creation of a common European indicator for fire danger. In Greece, the lab of forest informatics of the Democritus University of Thrace has developed decision support systems that are employing heuristic reasoning and fuzzy logic (fuzzy expected intervals) in order to estimate wild fire risk for the following year. The heuristic reasoning is based on the effect of political elections and drought cycles (following a periodicity of 3 to 5 years) in the number of forest fires in Greece [START_REF] Iliadis | Intelligent Information Systems in Risk Estimation Stamoulis Editors[END_REF].

Intelligent Information Systems

Fuzzy Algebra

Fuzzy logic [18], [START_REF] Cox | Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration[END_REF], [START_REF] Kecman | Learning and Soft Computing[END_REF], allows the definition of real world concepts, such as "area with high vulnerability to forest fires" in the form of fuzzy sets. Every member of the universe of discourse belongs to a fuzzy set with a different degree of membership, ranging from 0 to 1. The degree of membership can be estimated by the use of proper membership functions (MF). Fuzzy sets correspond to real life linguistics. Fuzzy logic is an human knowledge embodying tool through operational algorithms [START_REF] Iliadis | A decision support system applying an integrated Fuzzy model for long -term forest fire risk estimation[END_REF] [START_REF] Kecman | Learning and Soft Computing[END_REF]. In fuzzy algebra there are many kinds of membership functions but the most characteristic are the triangular, the trapezoidal ones and the family of the sigmoid functions. Sigmoid MF have been used in several research efforts in order to develop fuzzy inference systems [START_REF] Duprey | A Fuzzy Based Stability Index Using a Right Sigmoid Membership Function[END_REF]. This research effort has been implemented by applying three distinct fuzzy functions that all belong to the sigmoid family.

The functions of the Gaussian distribution curve family

The fuzzy toolbox of the Matlab platform has been used in order to obtain the membership degrees for each forest department, given by three MF that belong to the Gaussian distribution curve, namely the Gaussian, the Sigmoid, and the S-shaped one. The Gaussian fuzzy membership function (GFMF) is symmetrical and it depends on two parameters c and σ which represent the center and the width of a fuzzy set [START_REF] Pieczynski | Application of the General Gaussian Membership Function for the Fuzzy Model Parameters Tunning[END_REF]. More details can be seen in the following figure 2. Gaussian fuzzy membership functions are quite popular in the fuzzy logic literature, as they are the basis for the connection between fuzzy systems and radial basis function neural networks. A typical form of a GFMF can be seen in the following equation 1 [START_REF] Iliadis | Intelligent Information Systems in Risk Estimation Stamoulis Editors[END_REF].

    2 2 2 , ,   c x e c x f    (1)
The Sigmoid fuzzy membership function (SFMF) is given by the following equation 2. It is a continuous monotonic mapping of the input into a value between 0.0 and 1.0.

( ) 1 ( ; , ) 1 a x c f x a c e     (2)
In the case of the SFMF the parameters a, c define the schema and the position of the curve [START_REF] Iliadis | Intelligent Information Systems in Risk Estimation Stamoulis Editors[END_REF]. Depending on the sign of the parameter a, it is inherently open to the right or to the left, and thus it is appropriate for representing concepts such as "very large" or "very negative". The S-shaped membership function (SSFMF) is a spline-based curve and it is a special version of the Sigmoid one. The following table 1, presents the commands that were employed in MATLAB in order to perform the membership functions.

Table 1. Sample T-Norms

It should be specified that the parameters a and b locate the extremes of the sloped portion of the curve. The following figure 1 shows the actual shape of the three sigmoid membership function that have been applied.

Fuzzy membership function MATLAB"s implementation command GFMF

    , y Gaussmmf x sig c  SFMF     , y Sigmf x a c  SSFMF     , y Smf x a b 

Fuzzy Aggregation Operators

According to fuzzy algebra, every element of the universe of discourse can belong to a fuzzy set à and simultaneously to its complement C A ~ with a degree of membership complementary to 1. T-Norms are the fuzzy conjunction operators between fuzzy sets. Fuzzy algebra contains several T -Norms, each one of them offering a different approach of the fuzzy AND, operation [START_REF] Iliadis | Intelligent Information Systems in Risk Estimation Stamoulis Editors[END_REF], [START_REF] Kecman | Learning and Soft Computing[END_REF]. The following table 2 below contains equations 3 and 4 and it presents a small sample of the most common T-Norms. They have a wide range of applications including the evaluation of Artificial Neural Networks [START_REF] Iliadis | Application of fuzzy T-norms towards Artificial Neural Networks' evaluation: A case from wood industry[END_REF].

Table 2. Sample T-Norms

T-Norm name T-Norm equation Min (3)                                                   x x x x x x x B A , min | , ~      Drastic Product (4)   B A min{μ A ~(x), μ B ~(x)} if max{μ A ~(x), μ B ~(x)}=1 else   B A 0
The choice of the appropriate norm depends on the perspective under which the problem is examined. For example, if the developer needs an optimistic norm that will assign the least potential overall degree of risk, then the min T-norm should be applied, whereas if the developer wishes to distinguish the cases that are characterized by extreme values for one or more risk parameters, the drastic product is the proper norm to be employed.

Developing the fuzzy inference system

The risk estimation is based on historical data that refer to the annual forest fire frequency (FFF) and to the annual burned area (ABA) in each area under study. The fuzzy inference system has been developed in the MatlLab integrated environment and more specifically by writing MatLab code in the development environment and also by the use of the fuzzy toolbox for the construction of the fuzzy membership functions and for the Ruleset construction. The primitive data that have been used as input have been initially stored in Microsoft Excel sheets and they are input to the fuzzy inference system by employing commands of the type:

         FFF" to due risky "low .. .. 1 / ) ( 1 ~n i X A i i           FFF" to due "risky .. .. 1 / ) ( 1 ~n i X B i i           FFF" to due risky "extremely .. .. 1 / ) ( 1 ~n i X C i i           ABA" to due risky "low .. .. 1 / ) ( 2 ~n i X A i i           ABA" to due "risky .. .. 1 / ) ( 2 ~n i X B i i           ABA" to due risky "extremely .. .. 1 / ) ( 2 ~n i X C i i 
where n is the number of case under study. Each forest department belongs to all six fuzzy sets with a distinct degree of membership. Of course the characteristic linguistic that describes a case is the one with the highest degree of membership. This approach not only allows the proper definition of linguistics that show clearly the status of an area due to one factor, but it also enables the distinction between two cases of the same linguistic. For example if two forest departments are both high risky, their degree of membership determines which one is more risky than the other.

During the design of the fuzzy inference system, the developer has to input the maximum and the minimum annual values ever recorded in Greece for the forest fire frequency and for the total burned area. Then the fuzzy toolbox determines the values of the σ and c parameters of the Gaussian function and the parameter values α, c, used by the Sigmoid and the S-shaped membership functions. For the output of the system also three fuzzy sets corresponding to three linguistics have been defined namely:

         risk" integrated to due risky "low .. .. 1 / ) ( 3 ~n i X A i i           risk" integrated to due "risky .. .. 1 / ) ( 3 ~n i X B i i           risk" integrated to due risky "extremely .. .. 1 / ) ( 3 ~n i X C i i 
After the storage of the data in vectors and the definitions of the fuzzy membership functions the Ruleset has been constructed. Figure 3, presents the design of the Ruleset. Several approaches have been proposed lately in order to design decision tables and decision trees [START_REF] Kuncheva | An experimental study on Rotation Forest ensembles[END_REF]. In this case, due to the small number of parameters a rather heuristic approach has been followed in order to minimize the number of required rules as much as possible and to produce a quite rational system. The unification of the partial risk degrees due to the number of forest fire frequencies and to the total burned area to an integrated risk index has been performed by the system by the use of the minimum T-Norm.

Three distinct systems have been developed, each one using a specific sigmoid membership function and they have been saved as a ffriskGaus.fis, ffriskSigm.fis and ffriskSm.fis using the Gaussian, the Sigmoid and the S-shaped membership functions respectively. Each one of the developed fuzzy inference systems can be executed from the Matlab command line by using the commands readfis and evalfis.

For example the commands: fffrisk = readfis('ffriskGaus.fis'); and intergrated_risk = evalfis(ffriskGaus, fffrisk); have been used to execute the Gaussian system and they store the output (unified degrees of membership taking values from 0 to 1) into a proper matrix named integrated_risk. The results have been exported to sheets of Microsoft Excel again by using the MatLab command xlswrite.

Results -Discussion

The system has been tested and evaluated with actual data related to forest fire incidents in Greece for the period 1984-2007 which is a quite long time interval.

Conclusions

The annual "extremely risky" PRIs and the overall integrated "extremely risky" indices obtained by the system for each year were compared to the actually most risky areas based on the number of FFF and on the ABA for the following year in order to determine the validity of the system. As far as the Gaussmf curve is concerned, for the parameter FFF the percentages of successful risk characterization reaches as high as 70%. The same function for the parameter of the annual burned area offers a percentage of success equal to 48%. The Sigmoid function (Sigmf), for the parameter FFF has also a percentage of successful risk characterizations as high as 70%, but for the burned area the percentage is 51%. Finally Smf has a percentage of success as high as 74% for the number of forest fires and 46% for the burned area. During the period 1985-2007 the overall integrated risk index obtained by employing the min T-Norm offers an average accuracy of 65%, 54% and 52% for the cases of the Gaussian, Sigmoid and S-shaped membership functions respectively. The Gaussian function achieves the highest percentages of success towards overall risk estimation, whereas the other two functions give also satisfying results. The system will be extended by applying weights in the unification of the risk indices according to the importance of each factor.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Graphics of the three employed membership functions

Fig. 3 .

 3 Fig. 3. A sample of the Ruleset of the fuzzy inference system.

  This sample command imports data concerning burned areas for 1990 into a MATLAB vector named C. Several commands of this type have been written in order to store each column containing the annual FFF and the ABA in proper one dimensional Matrices (vectors). All of these commands have been stored in a MatLab programming file called Input_Data.m. The benefit from the creation of this file is that it runs just by typing the name of the file in the command line. For each one of the two input variables three fuzzy sets have been formed corresponding to proper Linguistics. The following six fuzzy sets have been formed, namely:

	 C xlsread data xls ' 1. ','1990',' 2 : 89' ;  B B

 

Table 3 .

 3 PRI based on the FFF using the Gaussian and S shaped functionsThe above Table3presents clearly the obtained partial risk indices based on the number of forest fire incidents" frequencies, with the use of both Gaussian an S-shaped membership functions only for the cases of the Extremely risky forest departments.

						GFMF	SFMF
			GFMF	SFMF		Extreme	Extreme
			Extremely	Extremely		ly risk	ly risky
		forest	risky	risky	forest	index	index
	Year	department	index FFF	index FFF Year	department	FFF	FFF
	1985	Pyrgos	0.9737	1 1999	Hleia	1	1
		Olympia	0.9538	0.966	Messinia	1	1
		Patra	0.8275		Argolida	0.9967	1
	1986	Olympia	0.9802	1 2000	Messinia	1	1
		Pyrgos	0.995	1	Korinthos	1	1
		Patra	0.956	0.9938	Hleia	0.9994	1
		Korinthos	0.9231	0.9753	Lakonia	0.9508	1
	1987	Pyrgos	1	1 2001	Messinia	1	1
		Olympia	0.9692	1	Korinthos	1	1
	1988	Olympia	0.9523	1	Arkadia	1	1
		Argolida	0.9692	0.962	Lakonia	0.9569	1
	1989	Pyrgos	0.9802	1 2003	Messinia	1	1
		Olympia	0.9802	1	Hleia	1	1
		Tripolh	0.9802	0.9988	Arkadia	0.9999	1
		Patra	0.956	1	Korinthos	0.9928	1
	1990	Pyrgos	0.9756	1 2004	Messinia	1	1
		Olympia	0.9756	0.9882	Hleia	1	1
	1991	Argolida	0.9692	0.9644	Korinthos	0.9889	0.9828
		Korinthos	0.9692	0.9644	Arkadia	0.9595	0.946
		Olympia	0.9321	1	Lakonia	0.9406	0.92
	1992	Korinthos	0.9978	1	Argolida	0.9231	1

Table 4 .

 4 PRI for the ABA and overall risk indices for the combination ofGFMF and Min (1985-2007)

	Year	Forest departmen t	GFMF Extre mely risky Partial index ABA	SSFM F Extre mely risky Partia l index ABA	OVE RALL risk inde GFM F and Min Norm	Year	Forest depart ment	GFMF Extrem ely risky Partial index ABA	SSFMF Extreme ly risky Partial index ABA	OVERA LL risk index GFMF and Min Norm
										XR
	1984 Kapandriti	1	1		1994 Patra	1	1	0.181
										XR
		Aigaleo	0.9817	1			Pendelh	1	1	0.606
		Korinthos	0.9247	1			Gytheio	1	1	R 0.323
					R
	1985 Aigaleo	1	1	0.150	1995 Patra	1	1	R 0.969
					XR					XR
		Megara	1	1	0.110		Gytheio	1	1	0.369
					XR					XR
		Patra	0.9999	1	0.827		Molaoi	0.9584	1	0.310
					XR		Kalama			XR
		Lavrio	0.9903	1	0.582		ta	0.9525	0.9191	0.952
					XR					XR
		Amaliada	0.9522	1	0.457	1996 Molaoi	1	1	0.230
					XR					XR
	1986 Korinthos	1	1	0.923		Patra	0.9718	1	0.234
					R		Korinth			XR
		Molaoi	0.9867	1	0.946		os	0.9969	0.9904	0.774
					XR		Olympi
		Olymbia	0.9356 0.9249	0.935	1997	a	1	1	XR 1
					XR
		Pyrgos	0.9097 0.8943	0.909		Gytheio	0.9886	1	R 0.946
					XR		Korinth			XR
	1987 Patra	1	1	0.681	1998	os	1	1	0.700
					XR					XR
		Kalamata	0.9868	1	0.754		Pendeli	1	1	0.290
					XR		Kapand
		Moaloi	1	1	0.457		riti	0.95	1	R 0.950
					XR					XR
		Argolida	0.9712 0.9675	0.339	1999 Lakonia	1	1	0.910
					R		Messhn			XR
	1988 Kalamata	1	1	0.216		ia	0.9679	1	0.967

The determination of the most risky areas based on partial risk indices (due to forest fire frequencies or due to the annual burned area) is similar regardless the use of the Gaussian, the Sigmoid or the S-shaped membership functions. However the S-shaped function assigns the highest risk value more often whereas the Gaussian one differentiates the forest departments more clearly by assigning them with a wide range of risk indices. Table 4 presents the partial risk indices for the extremely risky areas according to the annual burned area, in the cases of the Gaussian and of the S-shaped membership functions. The estimated overall risk indices" vector (obtained as the output of the fuzzy inference system) for the Gaussian membership function and for the Min T-Norm is also presented clearly in the above Table 4. It contains the most risky forest departments based on partial risk indices and also on the overall risk index (considering risk due to both FFF and ABA). It estimates their corresponding linguistics (risky R, or extremely risky XR) only for the Gaussian function due to the fact that it offers a more rational production of risk indices, whereas the other two functions assign the highest index with the value 1 for too many cases and thus there is no proper distinction between the cases. The determination of the unified overall risk indices has been performed by the fuzzy inference system based on the Ruleset which is presented in figure 3