Bruno Fève

Claire Bastard

Soraya Fellahi

Jean-Philippe Bastard

Jacqueline Capeau

New Adipokines Nouvelles adipokines

Keywords: adipocyte, adipokine, apelin, fibroblast growth factor-21, insulin resistance, neuroregulin-4, obesity, adipose tissue Résumé adipocyte, adipokine, apéine, fibroblast growth factor-21, insulinorésistance, neuroréguline-4, obésité, tissu adipeux

Adipose tissue is now widely recognized as "an organ" able to synthesize and secrete hundred factors collectively called adipokines. These secreted molecules exert pleiotropic actions, notably on the regulation of glucose and lipid metabolism, inflammation, reproduction, or angiogenesis. Over the past two decades, a considerable amount of work was performed on the two "star" adipokines, leptin and adiponectin, particularly because of their involvement in energy metabolism. The present review is focused on the three most recently discovered adipokines that are clearly emerging as important actors in metabolism: apelin, fibroblast growth factor-21, and neuroregulin-4. Moreover, given a number of clinical and experimental data, these three adipokines represent promising targets in the context of metabolic disorders associated with obesity.

Introduction

Over the last twenty years, considerable progresses have been made regarding the demonstration of the endocrine nature of adipose tissue (AT), dramatically illustrated in 1994 by the discovery of leptin, which exerts an anorectic effect on the central nervous system.

Other adipokines have also been extensively investigated as adiponectin, interleukin (IL)-6, IL-tumor necrosis factor (TNF)- monocyte chemoattractant protein (MCP)-1, resistin, omentin, or vaspin. However, we are far from understanding their pathophysiological implications. The complexity of this domain is documented by recent proteomic approaches, which indicate that human AT explants could secrete more than 700 distinct proteins.

Therefore, the biology of AT will become more and more complicated.

Adipokines regulate important biological processes in target organs such as the brain, liver, skeletal muscle, cardiovascular and immune systems, and the endocrine pancreas (Figure 1). This could explain the close link between obesity and the metabolic and cardiovascular complications [START_REF] Blüher | From leptin to other adipokines in health and disease: facts and expectations at the beginning of the 21 st century[END_REF][START_REF] Sahin-Efe | Advances in adipokines[END_REF]. The production of many adipokines is deregulated in obesity [START_REF] Blüher | Adipose tissue dysfunction in obesity[END_REF], and could participate into disturbances of appetite and satiety, and into changes in the distribution of AT, insulin secretion, insulin sensitivity, energy expenditure, endothelial function, angiogenesis, inflammation, blood pressure, haemostasis, osteoarticular functions and reproduction. Consequently, adipokines offer promising prospects for the management of obesity-related morbidities. Moreover, adipokines are not necessarily derived from adipocytes, but also from other celltypes present in AT that contains not only adipocytes (that represent less than half of the total number of cells present in the tissue), but also various amounts of immune cells (macrophages, lymphocytes, granulocytes, mast cells), endothelial cells, and fibroblasts.

Leptin and adiponectin are mainly derived from adipocytes, while the pro-inflammatory cytokines IL- IL-6, TNF- are primarily produced by macrophages and immune cells. In addition, the secretory profiles of this heterogeneous and plastic tissue may be different according to the location of fat deposits.

Finally, we must emphasize that new data and innovative concepts, well beyond the metabolic effects of these adipokines, have emerged over the last ten years. In this review article, we decided to focus on three "new" adipokines of interest which present potential therapeutic prospects: apelin, Fibroblast Growth factor (FGF)-21, and neuregulin-4.

Apelin

Discovery, structure and main functions

In 1998, Tatemoto et al. purified from bovine stomach extracts a peptide recognizing a previously discovered G protein-coupled orphan receptor, APJ, now designated the apelin receptor. APJ has a high homology with the type 1 receptor of angiotensin II (4). The apelin gene encodes a 77 amino acids protein called preproapelin (5) that undergoes a proteolytic processing giving rise to various biologically active forms of apelin: apelin 36, 17, 13, and pyroglutamate apelin-13, the latter being protected from rapid degradation by ectopeptidases.

Apelin is produced by AT (mainly adipocytes), but also by many other tissues such as lung, mammary gland, testis, muscle and brain. The apelin/APJ system is involved in a wide variety of functions such as cardiovascular, fluid, and angiogenic homeostasis (6.7).

The demonstration of apelin being secreted by adipocytes, and thus being an adipokine, was conducted in 2005 by the team of Valet et al. [START_REF] Boucher | Apelin, a newly identified adipokine up-regulated by insulin and obesity[END_REF]. We will focus here on the current knowledge of the physiology and pathophysiology of apelin regarding the energy balance.

Apelin and carbohydrate metabolism

An initial work characterized the inhibitory role of apelin on insulin secretion [START_REF] Winzell | The APJ receptor is expressed in pancreatic islets and its ligand, apelin, inhibits insulin secretion in mice[END_REF]. However, conversely, hypoglycemic properties of apelin were discovered in 2008 in mice [START_REF] Dray | Apelin stimulates glucose utilization in normal and obese insulin-resistant mice[END_REF], both in the fasted state and during a glucose tolerance test. This effect was observed both in obese insulin-resistant and in control mice. This was associated with increased glucose utilization by skeletal muscle and AT, and involved the phosphorylation of AMP-activated kinase (AMPK) as well as the activation of the endothelial nitric oxide (NO) synthase [START_REF] Dray | Apelin stimulates glucose utilization in normal and obese insulin-resistant mice[END_REF]. These data were confirmed latter [START_REF] Yue | Apelin is necessary for the maintenance of insulin sensitivity[END_REF], in particular by using KO mice for the preproapelin gene (apelin -/mice), which exhibit hyperinsulinemia and insulin resistance, decreased insulin sensitivity being exacerbated under high fat and high fructose diet [START_REF] Yue | Apelin is necessary for the maintenance of insulin sensitivity[END_REF].

The stimulatory effect of apelin on glucose transport in isolated murine adipocyte has not been currently documented, while apelin was shown to activate glucose transport in an AMPK-dependent manner in explants of human AT [START_REF] Attané | Apelin stimulates glucose uptake but not lipolysis in human adipose tissue ex vivo[END_REF]. This was also observed in the mouse 3T3-L1 adipocyte cell line, in which the process involves the phosphoinositide 3kinase (PI3K) and protein kinase B (AKT) pathway [START_REF] Zhu | Apelin stimulates glucose uptake through the PI3K/Akt pathway and improves insulin resistance in 3T3-L1 adipocytes[END_REF]. Apelin can also stimulate glucose transport and GLUT4 membrane translocation in the myocardium of C57BL / 6J mice [START_REF] Xu | In vivo, ex vivo, and in vitro studies on apelin's effect on myocardial glucose uptake[END_REF], and in the H9c2 cardiomyoblasts cell line [START_REF] Xu | In vivo, ex vivo, and in vitro studies on apelin's effect on myocardial glucose uptake[END_REF].

Apelin is also involved in intestinal glucose absorption. Glucose ingestion quickly triggers the secretion of apelin into the intestinal lumen of mice [START_REF] Dray | The intestinal glucose-apelin cycle controls carbohydate absorption in mice[END_REF]. Surprisingly, oral administration of apelin reduces the amount of the sodium glucose co-transporter SGLT1 at the enterocyte level, while GLUT4 is induced, which allows an increased intestinal absorption of glucose.

These results suggest that the entrance of carbohydrate in the intestine promotes its own absorption via the paracrine secretion of apelin, and accordingly insulin secretion. This could also be in agreement with the inductive effects of apelin on the secretion of the incretin, glucagon-like peptide (GLP)-1 [START_REF] Wattez | Apelin stimulates both cholecystokinin and glucagon-like peptide 1 secretions in vitro and in vivo in rodents[END_REF].

Studies evaluating the impact of apelin on glucose homeostasis have not systematically reported decreased fasting plasma glucose and insulin resistance in obese animals. By contrast, a decrease in plasma insulin in response to apelin was frequently observed in these models. This may be the result of either improved insulin sensitivity or an inhibitory effect of apelin on insulin secretion. Thus, apelin can reduce insulin secretion stimulated by different glucose concentrations [START_REF] Guo | Apelin inhibits insulin secretion in pancreatic beta-cells by activation of PI3-kinase-phosphodiesterase 3B[END_REF][START_REF] Ringström | Apelin is a novel islet peptide[END_REF].

Apelin and lipid metabolism

Apelin was shown to inhibit lipolysis stimulated by the -adrenergic agonist isoproterenol via Gq, Gi, and AMPK signaling in isolated rodent and mature 3T3-L1 adipocytes [START_REF] Yue | Apelin decreases lipolysis via G(q), G(i), and AMPK-dependent mechanisms[END_REF][START_REF] Than | Apelin inhibits adipogenesis and lipolysis through distinct molecular pathways[END_REF].

However, apelin has no effect on basal or isoproterenol-stimulated lipolysis in explants of human AT or isolated human adipocytes [START_REF] Attané | Apelin stimulates glucose uptake but not lipolysis in human adipose tissue ex vivo[END_REF]. The antilipolytic effect of apelin was found after a chronic treatment in mice [START_REF] Higuchi | Apelin, an APJ receptor ligand, regulates body adiposity and favors the messenger ribonucleic acid expression of uncoupling proteins in mice[END_REF] and in transgenic mice overexpressing apelin and fed a high fat diet [START_REF] Yamamoto | Apelin-transgenic mice exhibit a resistance against diet-induced obesity by increasing vascular mass and mitochondrial biogenesis in skeletal muscle[END_REF].

A chronic treatment of insulin-resistant obese mice by apelin increases fatty acid oxidation in the skeletal muscle through activation of AMPK [START_REF] Attané | Apelin treatement increases complete fatty acid oxidation, mitochondrial oxidative capacity, and biogenesis in muscle of insulin-resistant mice[END_REF]. Moreover, this treatment can prevent a reduction in fatty acid and glucose oxidation in a model of heart failure related to obesity [START_REF] Alfarano | Transition from metabolic adapatation to maladaptation of the heart in obesity : role of apelin[END_REF]. In addition to the induction of fat utilization, apelin increases mitochondrial biogenesis in muscle [START_REF] Attané | Apelin treatement increases complete fatty acid oxidation, mitochondrial oxidative capacity, and biogenesis in muscle of insulin-resistant mice[END_REF] and cardiomyocytes [START_REF] Alfarano | Transition from metabolic adapatation to maladaptation of the heart in obesity : role of apelin[END_REF] by a mechanism that requires induction of peroxisome proliferator-activated receptor- co-activator (PGC)- Surprisingly, the resistance to obesity of transgenic mice overexpressing apelin is correlated with an increase in their muscle vasculature. The importance of apelin in maintaining the integrity of the blood and lymph systems was recently observed in apelin -/-mice [START_REF] Sawane | Apelin inhibits diet-induced obesity by enhancing lymphatic and blood vessel integrity[END_REF]. In fact, their exaggerated weight gain could be related to an enhanced vascular permeability, which in turn would promote the uptake of fatty acids by AT [START_REF] Sawane | Apelin inhibits diet-induced obesity by enhancing lymphatic and blood vessel integrity[END_REF]. Thus, apelin would prevent obesity while preserving the integrity of the vascular network.

Energy expenditure in response to apelin was also investigated on the thermogenic aspect.

Rectal temperature and oxygen consumption are greater in mice treated with apelin and receiving a normal diet, presumably through induction of uncoupling protein (UCP)1 in brown adipose tissue [START_REF] Higuchi | Apelin, an APJ receptor ligand, regulates body adiposity and favors the messenger ribonucleic acid expression of uncoupling proteins in mice[END_REF]. This increase in body temperature and oxygen consumption is also found in transgenic mice overexpressing apelin and receiving a high fat diet [START_REF] Yamamoto | Apelin-transgenic mice exhibit a resistance against diet-induced obesity by increasing vascular mass and mitochondrial biogenesis in skeletal muscle[END_REF], but is not observed in a model of insulin-resistant obese mice receiving a chronic treatment with apelin [START_REF] Attané | Apelin treatement increases complete fatty acid oxidation, mitochondrial oxidative capacity, and biogenesis in muscle of insulin-resistant mice[END_REF].

Variations of plasma apelin in human disease

Many studies have reported increased plasma concentrations of apelin in obese or diabetic patients [START_REF] Castan-Laurell | Apelin, diabetes, and obesity[END_REF]. Apelin 17 and pyroglutamate apelin 13 constitute the main plasma forms.

According to recent data in diabetic patients, the plasma apelin level seems to be a new predictive biomarker of diabetes in ethnic Chinese Han [START_REF] Ma | Plasma apelin : a novel biomarker for predicting diabetes[END_REF]. Apelin plasma levels are higher in type 1 diabetic patients compared to controls, and even higher than in type 2 diabetes (T2D) [START_REF] Habchi | Circulating apelin is increased in patients with type 1 or type 2 diabetes and is associated with better glycemic control[END_REF], which is in agreement with a previous work in type 1 diabetes (T1D) [START_REF] Alexiadou | Differences in plasma apelin and visfatin levels between patients with type 1 diabetes mellitus and healthy subjects and response after acute hyperglycemia and insulin administration[END_REF].

What could be the meaning of a high value of apelinemia? Is obesity implicated? Habchi et al [START_REF] Habchi | Circulating apelin is increased in patients with type 1 or type 2 diabetes and is associated with better glycemic control[END_REF] showed that circulating apelin concentrations were negatively correlated with glycated haemoglobin (HbA1c) in T2D, suggesting that apelinemia was associated with a better glycemic control. In T1D, the elevation of apelin might compensate for the lack of insulin but may also be explained by the insulin treatment, which is a powerful positive effector of the synthesis and secretion of apelin [START_REF] Boucher | Apelin, a newly identified adipokine up-regulated by insulin and obesity[END_REF]. Furthermore, T1D patients are generally non-obese, suggesting that obesity is probably not a major determinant of plasma apelin. In fact, no correlation between BMI and apelinemia has been described [START_REF] Castan-Laurell | Apelin, diabetes, and obesity[END_REF]. In a recent work Krist et al [START_REF] Krist | Effects of weight loss and exercise on apelin serum concentrations and adipose tissue expression in human obesity[END_REF] evaluated whether, in the context of weight reduction (bariatric surgery, physical exercise or caloric restriction), changes in apelinemia were mainly related to weight reduction or rather reflected a better sensitivity to insulin. Regardless of the type of strategy to reduce weight, lower apelin plasma levels were observed, as previously described [START_REF] Castan-Laurell | Apelin, diabetes, and obesity[END_REF][START_REF] Heinonen | Effects of diet-induced weight loss on plasma apelin and cytokine levels in individuals with metabolic syndrome[END_REF]. Furthermore, plasma apelin levels are related to improved insulin sensitivity independently of BMI [START_REF] Heinonen | Effects of diet-induced weight loss on plasma apelin and cytokine levels in individuals with metabolic syndrome[END_REF].

Thus, the elevation of apelinemia observed in T2D could be, as in T1D, an adaptive mechanism to directly reduce insulin resistance and when insulin resistance is reduced, this would then allow a decrease in apelinemia.

The metabolic effects of apelin described in different models emphasize its beneficial role in both energy balance and insulin sensitivity. To understand its involvement in human pathophysiology, it will be necessary to develop more reliable immunoassays to measure apelinemia. In parallel, the use of selective agonists or antagonists of APJ will clarify the involvement of this system in energy balance, and allow the development of original therapeutic strategies.

Fibroblast Growth factor-21 (FGF21)

The FGF family FGF21 was identified as a metabolic effector with many properties. It is able to induce glucose transport in adipocytes, to improve glucose tolerance, insulin sensitivity and lipid profile, and to reduce body mass [START_REF] Kim | FGF21 as a stress hromone : the roles of FGF21 in stress adpatation and the treatment of metabolic diseases[END_REF][START_REF] Gimano | FGF21-based pharmacotherapy-potentially utility for metabolic disorders[END_REF][START_REF] Itoh | FGF21 as a hepatokine, adipokine, and myokine in metabolism and diseases[END_REF]. As explained below, the mechanisms of these effects are well deciphered and involve pleiotropic actions in adipose tissue, liver, pancreas and hypothalamus. Although most of the data were obtained in rodent models, there are also data in primates and in humans, which suggest a favorable metabolic effect of this molecule.

The FGF family includes 23 members (FGF1 to FGF23) that can be classified according to their mode of action, autocrine, paracrine and endocrine. Endocrine FGF include FGF19 (and its murine orthologue FGF15), FGF21 and FGF23. While most of the paracrine and endocrine FGF possess mitogenic properties, FGF21 is unique in its metabolic properties and its lack of proliferative effect.

Signaling mechanisms of FGF21

It is now well established that the metabolic effects of FGF21 require the binding to and the activation of the receptor FGFR1c in cooperation with -Klotho [START_REF] Ogawa | Beta-Klotho is required for metabolic activity of fibrobalst growth factor 21[END_REF][START_REF] Kharitonenkov | FGF-21/FGF-21 receptor interaction and activation is determined by beta-Klotho[END_REF][START_REF] Adams | FGF21 requires beta-Klotho to act in vivo[END_REF]. Co-expression of FGFR1c and -Klotho in AT, liver, muscle pancreas, hypothalamus and brainstem is required for the action of FGF21 in these tissues.

The interaction of FGF21 with FGFR1c and -Klotho allows FGFR1c autophosphorylation and activation of various downstream phosphorylation pathways comprising the FGF receptor substrate (FRS2), ERK1/2 kinases (extracellular signal-regulated kinase 1 and 2), GSK3 (glycogen synthase kinase-3), AKT (protein kinase B), p70 S6K, Raf, SHP2 (Src-homology domain-2-containing phosphatase 2), and the STAT3 transcription factor (Signal transducer and activator of transcription-3) [START_REF] Gimano | FGF21-based pharmacotherapy-potentially utility for metabolic disorders[END_REF]. Activation of these pathways induces the expression of many genes.

Tissues and actors relaying the metabolic effects of FGF21

The administration of FGF21 causes a rapid induction of the glucose transporter GLUT1 in white adipose tissue (WAT) [START_REF] Kharitonenkov | FGF-21 as a novel metabolic regulator[END_REF][START_REF] Ge | Fibroblast growth factor 21 induces glucose transporter-1 expression through activation of the serum response factor/Etslike protein-1 in adipocytes[END_REF]. More prolonged treatment (3 days) results in a thermogenic effect not only in brown adipose tissue (BAT) but also in WAT, with the morphological changes characteristic of an AT "browning" [START_REF] Chau | Fibroblast growth factor 21 regulates energy metabolism by activating the AMPK-SIRT1-PGC-1alpha pathway[END_REF][START_REF] Fisher | FGF21 regulates PGC-1 and browning of white adipose tissues in adaptive thermogenesis[END_REF]. An induction of lipogenesis and lipolysis is also observed in WAT.

AT is essential to target metabolic actions of FGF21, as shown in the model of AT-specific knockout of -Klotho since insulin-sensitizing effects of FGF21 overexpression are abolished in this model [START_REF] Ding | Beta-Klotho is required for fibroblast growth factor 21 effects on growth and metabolism[END_REF]. Similarly, deletion of FGFR1 in AT precludes the beneficial effects of FGF21 on insulin sensitivity, as well as most of its effects on weight loss and circulating lipid and hepatic changes [START_REF] Adams | The breadth of FGF21's metabolic actions are governed by FGFR1 in adipose tissue[END_REF][START_REF] Foltz | Treating diabetes and obesity with a FGF21-mimetic antibody activating the Klotho/FGFR1c receptor complex[END_REF]. This suggests that much of the effects of FGF21 on hepatic metabolism involves its action on adipocytes, and probably in part its ability to induce WAT browning.

Interestingly, adiponectin might represent one of the effectors of FGF21 in adipocytes. Indeed, the administration of FGF21 causes rapid secretion of this adipokine, and adiponectin knockout mice become resistant to the beneficial effects of FGF21 on lipid metabolism.

FGF21 is highly expressed in the pancreas, but its pharmacological actions on this organ are still poorly understood. FGF21 induces insulin gene expression and protect  cells from apoptosis in rat pancreatic islets and -cell lines [START_REF] Wente | Fibrobalst growth factor-21 improves pancreatic beta-cell function and survival by activation of extracellular signal-regulated kinase ½ and Akt signaling pathways[END_REF]. Although FGF21 does not increase insulin secretion in normal islets, it potentiates insulin secretion stimulated by glucose in diabetic mice islets, suggesting that FGF21 could avoid beta cell dysfunction [START_REF] Wente | Fibrobalst growth factor-21 improves pancreatic beta-cell function and survival by activation of extracellular signal-regulated kinase ½ and Akt signaling pathways[END_REF]. In addition, FGF21 reduced glucagon secretion in rodents and monkeys (39.46). Some metabolic actions of FGF21 may involve direct effects in the brain. Intracerebroventricular infusion of FGF21 in rats increases energy expenditure and insulin sensitivity [START_REF] Sarruf | Fibroblast growth factor 21 action in the brain increases energy expenditure and insulin sensitivity in obese rats[END_REF]. FGF21 is detected in human cerebrospinal fluid, and can cross the bloodbrain barrier. It is not detected in vivo in neurons, but can be strongly induced in neuronal cultures. Recent evidence suggests that FGF21 signalling in the hypothalamus and/or the brainstem is necessary for non-metabolic functions such as the control of female fertility, growth, or of the HPA axis. However, the neuronal FGF21/-Klotho signalling does not seem necessary to modulate the insulin-sensitizing effects of FGF21 [START_REF] Ding | Beta-Klotho is required for fibroblast growth factor 21 effects on growth and metabolism[END_REF].

Physiological functions of endogenous FGF21

FGF21 expression is preferentially expressed in the pancreas, liver, and AT, but the relative contribution of these different tissues to systemic levels of FGF21 remains unknown. Another important question is whether FGF21 acts as a paracrine or endocrine factor.

A major physiological characteristic of FGF21 is its induction during a prolonged fasting. It has recently been documented that it is primarily the protein restriction, and not the overall caloric restriction, which is responsible for a marked induction of liver and plasma FGF21 [START_REF] Laeger | FGF21 is an endocrine signal of protein restriction[END_REF]. Mice overexpressing FGF21 exhibit a phenotype reminiscent of prolonged fasting, with a slowdown in growth, female infertility, a state of torpor. In this context, impaired GH signalling (47) may contribute to longer life expectancy [START_REF] Zhang | Associations of fibroblast growth factor 21 gene 3' untranslated region single-nucleotide polymorphisms with metabolic syndrome, obesity, and diabetes in a Han Chinese population[END_REF]. FGF21 seems to be a factor involved in the metabolic adaptation to fasting situations, especially in the case of protein restriction.

FGF21 is also an induced under many other stressful situations, such as exposure to cold, exercise and nutritional excess. The endoplasmic reticulum stress secondary to abnormalities in lipid metabolism or mitochondrial dysfunction greatly increases the expression of FGF21, which could participate to an appropriate metabolic response.

FGF21 in human diseases

Currently there is no clear association between the genetic components of the FGF21 signalling pathway and hereditary diseases. However, a polymorphism in a FGF21 exon was found to be associated with carbohydrate food intake [START_REF] Chu | Novel locus including FGF21 is associated with macronutrient intake[END_REF] and a polymorphism in the 3 'noncoding region was associated with the metabolic syndrome, obesity, and diabetes [START_REF] Zhang | Associations of fibroblast growth factor 21 gene 3' untranslated region single-nucleotide polymorphisms with metabolic syndrome, obesity, and diabetes in a Han Chinese population[END_REF].

Moreover, changes in circulating levels of FGF21 have been reported in situations of altered metabolism leading to consider this hormone as a new biomarker. However, the interest of FGF21 is limited by the high inter-individual variability of the plasma concentrations (0.05 to 5.5 ng / ml) in healthy individuals. Importantly, it was observed that circulating levels of FGF21 are 20-50% higher in obese patients or T2D compared to healthy subjects [START_REF] Bobbert | Fibroblast growth factor 21 predicts the metabolic syndrome and type 2 diabetes in caucasians[END_REF][START_REF] Chen | High plasma level of fibroblast growth factor 21 is an independent predictor of type 2 diabetes : a 5.4-year population-based prospective study in Chinese subjects[END_REF][START_REF] Xiao | Distinct changes in serum fibroblast growth factor 21 levels in different subtypes of diabetes[END_REF][START_REF] Dushay | Increased fibroblast growth factor 21 in obesity and nonalcoholic fatty liver disease[END_REF] suggesting that FGF21 could be an independent predictor of T2D and metabolic syndrome [START_REF] Bobbert | Fibroblast growth factor 21 predicts the metabolic syndrome and type 2 diabetes in caucasians[END_REF][START_REF] Chen | High plasma level of fibroblast growth factor 21 is an independent predictor of type 2 diabetes : a 5.4-year population-based prospective study in Chinese subjects[END_REF], while T1D patients have lower plasma levels of FGF21 [START_REF] Xiao | Distinct changes in serum fibroblast growth factor 21 levels in different subtypes of diabetes[END_REF].

Increased plasma FGF21 levels were also reported in the Cushing's syndrome [START_REF] Durovcová | Plasma concentrations of fibroblast growth factors 21 and 19 in patients with Cushing's syndrome[END_REF], in women in pre-eclampsia [START_REF] Stepan | Serum levels of the adipokine fibroblast growth factor-21 are increased in preeclampsia[END_REF], while anorexia nervosa was associated with a FGF21 decrease [START_REF] Dostálová | Plasma concentrations of fibroblast growth factors 19 and 21 in patients with anorexia nervosa[END_REF].

Is FGF21 a promising therapeutic target?

In view of the beneficial metabolic effects of FGF21, several pharmaceutical companies developed FGF21 analogues, particularly with a longer half-life than the native molecule.

In addition antibodies with agonist properties on FGFR1 or -Klotho were developed. In particular, a monoclonal antibody capable of binding with high affinity to -Klotho activates the FGFR1/-Klotho signalling pathway and exerts favorable metabolic effects in the cynomolgus monkey [START_REF] Foltz | Treating diabetes and obesity with a FGF21-mimetic antibody activating the Klotho/FGFR1c receptor complex[END_REF].

Another possibility to enhance the action of FGF21 is to increase its endogenous levels by increasing its synthesis and/or inhibiting its degradation. However, this approach is complicated by the lack of knowledge of the tissues that contribute to circulating levels of FGF21, the respective roles of circulating and local forms of this factor, and the proteases involved in its degradation. Recently, it was nevertheless proposed that oxyntomodulin can reduce body weight by activating the transcription and secretion of liver FGF21 [START_REF] Habegger | Fibrobalst growth factor 21 mediates specific glucagon actions[END_REF].

The first proof of concept clinical study was published in 2013 by using a daily subcutaneous injection of the FGF21 analogue LY2405319. During a phase IB clinical study [START_REF] Gaich | The effects of LY2405319, an FGF21 analog, in obese human subjects with type 2 diabetes[END_REF], 46 obese patients with T2D were randomized between placebo and three doses of LY2405319 (3, 10, and 20 mg/day) for 28 days. Eight patients discontinued treatment, one due to a hypersensitivity attributed to the drug. Significant effects on LDL-cholesterol (-29%), triglycerides (-46%) and HDL cholesterol (+20%) were observed. In addition, a small but significant reduction in weight was observed. Although there was no significant change in blood glucose, lower insulin levels strongly suggest improved insulin sensitivity. There results on the beneficial metabolic effects of the FGF21 analogue in obese and diabetic patients are encouraging.

The neuroregulin-4 (Nrg4), a new adipokine that targets the liver

This last example of a very recently discovered adipokine (60) illustrates the interest and power of 'omics' approaches to identify new adipokines of unknown function.

The authors specifically identified proteins synthesized and secreted by BAT, whose major function is to ensure thermogenesis assuming that BAT would be capable of secreting factors acting at a distance to modulate energy homeostasis. The results highlighted that neuroregulin-4 (Nrg4), which preserves energy balance by limiting hepatic lipogenesis, was preferentially secreted by BAT.

At first, they performed a transcriptomic analysis of the mRNAs that are strongly induced during differentiation of brown murine preadipocytes in vitro. The analysis was oriented towards the identification of mRNA which structure predicted secreted factors. After a stringent selection, Nrg4 was identified being expression with a prominent expression in BAT, compared to WAT and other tissues.

Furthermore, the expression of Nrg4 was induced after cold exposure or after treatment of brown adipocytes in culture by norepinephrine.

Nrg4 belongs to a protein family containing epidermal growth factor (EGF)-like motifs, which are synthesized as transmembrane precursors and undergo proteolytic processing. The fragment released extracellularly then acts on the target cells as an autocrine/paracrine or endocrine factor. Nrg4 secretion was recovered in the culture medium of transfected cells overexpressing this factor.

The neuregulins transmit their signal through activation of ErbB receptors, and particularly of the ErbB4 form. Using the conditioned medium of Nrg4-overexpressing cells it was found that Nrg4 activated phosphorylation of ErbB3 and ErbB4 selectively in cells that express these receptors.

To assess whether Nrg4 was involved in the thermogenic function of BAT, wild mice or knockout Nrg4 (Nrg4 -/-) were exposed to cold. No difference in rectal temperature was detected between wild type or invalidated animals during exposure to cold, or in the expression of the uncoupling protein UCP1 in BAT. These data suggest that Nrg4 is not directly involved in thermogenesis in BAT, but may act on other tissues after being secreted by adipocytes.

Accordingly, in order to identify Nrg4-target organs, the authors generated a fusion protein between Nrg4 and alkaline phosphatase, and then measured the ability of Nrg4 to bind to tissues by histochemical studies. This elegant approach showed that Nrg4 binds significantly and specifically to the liver. This binding was greatly reduced when it was measured in the presence of an excess of the extracellular binding domains of ErbB3 or ErbB4. These data indicate that the liver is a target tissue of Nrg4, probably due to its binding to receptors of the ErbB family.

To explore the role of Nrg4 in energy balance, normal mice or Nrg4 -/-mice were subjected to a normal or a high fat diet. With the standard chow, there was no difference in weight between the two genotypes. By contrast, during a high fat diet, the Nrg4 -/-mice exhibited a greater weight gain, increased body fat, and a reduction in lean body mass. The plasma triglyceride levels were also higher as were blood glucose and fasting insulin. Accordingly, the glucose tolerance tests or insulin sensitivity indicated that Nrg4 deficiency exacerbated glucose intolerance and insulin resistance in mice fed high fat diet. Regarding the liver, the Nrg4 -/-mice had elevated triglyceride content and increased plasma concentration of alanine aminotransferase. This effect was not related to liver Nrg4 invalidation because it was not possible to reproduce it after injection of a small interfering RNA of Nrg4 specifically targeting the liver. Interestingly, a large study of gene expression in the liver of these animals indicated that the absence of Nrg4 was associated with induction of mRNA of many actors of the lipogenic pathway (fatty acid synthase, acetyl-CoA carboxylase, malic enzyme, stearoyl-CoA desaturase-1 ...). This was secondary to a major increase in the transcriptional factor controlling lipogenesis, SREBP1. By contrast, in Nrg4 knockout, the mRNA expression of genes involved in fatty acid oxidation, gluconeogenesis, or mitochondrial oxidative phosphorylation remained unmodified. The absence of Nrg4 therefore results in abnormal induction of hepatic lipogenesis and predisposes the animals to high fat diet-induced fatty liver.

In order to explore a direct action of Nrg4 on hepatic lipogenesis, primary cultures of mouse hepatocytes expressing ErbB4 receptor were used. Under these conditions, lipogenesis induced by an agonist of the LXR nuclear receptor was markedly inhibited in the presence of Nrg4, which behaves as a potent anti-lipogenic effector, causing trans-repression of gene encoding LXR.

It was important to analyse possible variations of Nrg4 expression under pathological metabolic conditions, foremost during obesity. In mice with high fat diet or genetically obese ob/ob and db/db, Nrg4 expression was strongly reduced in the epididymal WAT, but also in BAT. In a large cohort of subjects with a wide range of BMI, the expression of the Nrg4 mRNA in the subcutaneous AT was negatively correlated with the body mass index and hepatic lipid content. In addition, after matching on BMI, the expression of Nrg4 mRNA levels was lower in patients with impaired glucose tolerance or T2D than in individuals with normal glucose tolerance. These observational data in humans, associated with the liver phenotype of Nrg4 deficient mice, suggest that inadequate Nrg4 expression in AT could be involved in the pathogenesis of non-alcoholic fatty liver disease.

Accordingly, it was possible to anticipate that Nrg4 overexpression could prevent metabolic disorders associated with obesity. Mice overexpressing Nrg4 in their AT were thus generated.

During normal diet or as a result of exposure to cold, no abnormalities were detected between the two genotypes. By contrast, the transgenic mice have a significantly lower weight gain, and most have a frank reduction of fatty liver and plasma triglycerides under a high fat diet.

Mirror of what was observed in Nrg4 -/-mice, mice overexpressing Nrg4 in their AT have a significant decrease in the expression of genes involved in hepatic lipogenesis, such as SREBP1. In obesity induced by high fat diet, Nrg4 overexpression in AT is sufficient to limit lipogenesis and hepatic steatosis, and to improve glucose tolerance and insulin sensitivity.

Therefore, the discovery of this new adipokine with potent liver antilipogenic activity and favorable effects on glucose and lipid metabolism offers new therapeutic opportunities in the context of non-alcoholic steatohepatitis.

Conclusion

The obesity treatments have limited effectiveness on the long time (diet, physical activity, pharmacological treatment), or are associated with significant morbidity and mortality (bariatric surgery). It therefore remains crucial to develop new anti-obesity therapeutic strategies. Adipokines have demonstrated their potential roles in the regulation of appetite, satiety, energy expenditure, or inflammation and thus constitute prime targets for the treatment of obesity and its comorbidities. After the discovery of leptin more than twenty years ago, the field of investigation in the world of adipokines continues to expand, and gives hope for future progress in pathophysiological understanding and therapeutic.


Didier Dubois

Henri Prade

The first steps in fuzzy set theory in France forty years ago (and before) *

Keywords: fuzzy set, fuzzy logic, history

At the occasion of the fiftieth anniversary of the founding article "Fuzzy sets" by L. A. Zadeh, we briefly outline the beginnings of fuzzy set research in France, taking place some ten years later, pointing out the pioneering role of Arnold Kaufmann and few others in this emergence. Moreover, whe also point out that the French counterpart of the name "fuzzy set" had appeared some 15 years before Zadeh's paper, in a paper written in French by the very person who also invented triangular norms in the 1940's.

1 Before the beginning Strangely enough, the phrase "ensembles flous" (the French translation of "fuzzy sets") first appeared in a paper published in French in the Compte-Rendus of the French Academy of Sciences in 1951 [START_REF] Menger | Ensembles flous et fonctions aléatoires[END_REF] by Karl Menger (1902-1985). He was an Austrian mathematician [START_REF]Karl Menger[END_REF] who emigrated to the USA before the second World War. He is the son of the well-known economist Carl Menger (1840Menger ( -1921) ) himself one of the fathers of the theory of subjective utility value. Karl Menger was an active member of the Vienna Circle; later he was at the origin of triangular norms with the paper "Statistical metrics" [START_REF] Menger | Statistical metrics[END_REF], where triangular norms emerge in stochastic geometry from the generalization of the classical triangle inequality when distances between two elements of a metric space are represented by probability distributions rather than by numbers. His spectrum of interest, which was very wide [START_REF] Menger | Selected Papers in Logic and Foundations, Didactics, Economics[END_REF], included logic. He especially proposed a "logic of the doubtful" where (italics are from Menger himself):

we divide the propositions into three mutually exclusive classes of modality: µ + consisting of the asserted, µ 0 consisting of the doubtful, µ -consisting of the negated propositions. [• • • ] In contrast to the traditional 3-valued logic, the modality of a compound is not determined by the modalities of the components." [START_REF] Menger | A logic of the doubtful on optative and imperative logic[END_REF] He was thus making it clear very early that uncertainty is not compositional.

What is truly remarkable in Menger's 1951 paper is not only the use of the French counterpart to "fuzzy sets", but also its application to a notion closely related to Zadeh's idea: in fuzzy set terminology, the paper is about maxproduct transitive fuzzy relations! However, in Menger's paper, we can read (p.

2002):

Nous appellerons cette fonction même un ensemble flou et nous interpréterons Π F (x) comme la probabilité que x appartienne à cet ensemble. Si Π F ne prend que les valeurs 1 et 0, il s'agit essentiellement d'un sous-ensemble de U au sens classique et nous parlerons d'ensemble rigide. 2Moreover, Menger was soon aware of the emergence of fuzzy sets since one year after the publication of Zadeh's seminal paper [START_REF] Zadeh | Fuzzy sets[END_REF], he wrote [START_REF] Menger | First half entitled "Positivistic geometry" reprinted as "Geometry and positivism. A probabilistic microgeometry[END_REF]:

In 1951, I suggested that, besides studying well-defined sets, it might be necessary to develop a theory in which the element-set-relation is replaced by the probability an element belonging to a set. In a Paris note [Ref] 3 , I called such an object, in contrast to an ordinary or rigid set, ensemble flou (= hazy set)." In a slightly different terminology, this idea was recently expressed by Bellman, Kalaba and Zadeh [Ref] 4 under the name of fuzzy set. (These authors speak of the degree rather than than the probability an element belonging to a set.) Thus, the distinction between probability and degree of membership was very clear for Menger from the beginning; see [START_REF] Dubois | Fuzzy sets: History and basic notions[END_REF][START_REF] Seising | The genesis of fuzzy sets and systems -Aspects in science and philosophy[END_REF] for further discussions.

A worth noticing coincidence took place on May 28, 1951, the day when the French mathematician Arnaud Denjoy (1884-1974) transmitted Karl Menger's communication on "ensembles flous" to the French Academy of Sciences. Indeed, Arnaud Denjoy also transmitted on the same day a communication by Gustave Choquet [START_REF]Ensembles boréliens et analytiques dans les espaces topologiques[END_REF] whose abstract was En vue d'une théorie des fonctions non additives d'ensembles, on définit et l'on étudie la classe des sous-ensembles des espaces séparés engendrée à partir des compacts par réunions ou intersections dénombrables et par applications continues" 5Thus on the same day where the phrase "ensemble flou" appeared, elements towards the theory of capacities (i.e., "fuzzy measures" in Sugeno's terminology [START_REF] Sugeno | Theory of Fuzzy Integrals and its Applications[END_REF]) and Choquet integrals [START_REF] Choquet | Theory of capacities[END_REF] (which would appear later as the quantitative counterpart of Sugeno integrals) were also presented. The fuzzy future thus began on May 28, 1951, even if several decades and a significant research effort would still be necessary before the full landscape could be put together.

Besides, another piece of early work, apparently written independently from Zadeh's pioneering paper, is also worth mentioning. It is an article in French published in 1968 by a French linguist, Yves Gentilhomme (b. in 1920) in a Romanian journal [START_REF] Gentilhomme | Les ensembles flous en linguistique[END_REF]. In this paper, Gentilhomme calls "ensemble flou" a nested pair of subsets, one gathering what he regards as "the central elements", while the second larger subset also includes "peripheral elements". Gentilhomme motivates his proposal by an example of "hypergrammaticality" in texts (illustrated by a poem by Alphonse Allais where the author intentionally makes an abusive use of the imperfect tense of the subjunctive mood in order to produce a comical effect) and by an example of more or less credible words in French built from the same root. Then Gentilhomme provides a formal set-theoretic apparatus for combining his "ensembles flous", and he proposes to assign a degree of membership equal to 1/2 to peripheral elements (those that are not central). It is in the 1974 pioneering research monograph by Negoita and Ralescu [START_REF] Negoita | Multimi vagi si aplicatiile lor. (Ensembles flous et leurs applications)[END_REF] (who were working in Romania at that time) that Gentilhomme's paper is first reported and put in relation with Zadeh's work; "ensembles flous" are translated by "flou sets" in the English version of the book the year after [START_REF] Negoita | Application of Fuzzy Sets to Systems Analysis[END_REF].

Arnold Kaufmann

Edwin Diday (b. 1940) seems to have published the first journal paper in France influenced by the fuzzy set idea [START_REF] Diday | Optimisation en classification automatique et reconnaissance des formes[END_REF] in 1972. The paper presents a new approach to (fuzzy) clustering, called the dynamical cloud method (in French, "méthode des nuées6 dynamiques"), and cites Zadeh [START_REF] Zadeh | Fuzzy sets[END_REF] and Ruspini [START_REF] Ruspini | Numerical methods for fuzzy clustering[END_REF].

However, it is Arnold Kaufmann (1911Kaufmann ( -1994) ) [27,[START_REF] Dubois | In memoriam: Arnold Kaufmann[END_REF] who unquestionably introduced fuzzy set theory in France. He was an applied mathematician, author, or co-author of a long series of books covering many areas in engineering mathematics, including automatic control and operations research. His books, many of which were translated into English, were not only covering standard applied mathematics, but also many advanced topics in relation with current research at that time [START_REF] Denis-Papin | Cours de calcul matriciel appliqué[END_REF][START_REF] Denis-Papin | Cours de calcul tensoriel appliqué (géométrie différentielle absolue)[END_REF][START_REF] Denis-Papin | Cours de calcul booléien appliqué (notions sur les ensembles et les treillis, algèbres booléiennes, algèbre binaire)[END_REF][START_REF] Kaufmann | Les Phénomènes d'attente. Théorie et applications[END_REF][START_REF] Kaufmann | Analyse des réseaux électriques à tubes et à transistors[END_REF][START_REF] Kaufmann | Methods and Models of Operations Research[END_REF][START_REF] Kaufmann | Dynamic Programming: Sequential Scientific Management[END_REF][START_REF] Kaufmann | L'Homme d'Action et la Science[END_REF][START_REF] Kaufmann | The Science of Decision-Making. An introduction to praxeology[END_REF][START_REF] Kaufmann | Invitation à la recherche opérationnelle[END_REF][START_REF] Kaufmann | Introduction to operations research[END_REF][START_REF] Kaufmann | Exercices de calcul des probabilités[END_REF][START_REF] Kaufmann | Graphs, Dynamic Programming and finite games[END_REF][START_REF] Kaufmann | Méthodes et Modèles de la Recherche Operationnelle (Les Mathématiques de l'Entreprise[END_REF][START_REF] Kaufmann | Points and Arrows: Theory of Graphs (Student Library)[END_REF][START_REF] Kaufmann | Reliability: A Mathematical Approach[END_REF][START_REF] Kaufmann | Integer and Mixed Programming Theory and Applications[END_REF] 7 . As he was in contact with Lotfi Zadeh, he heard about fuzzy sets very early, and was quickly enthusiastic about this challenging way of thinking. He was the first in the world to publish a monograph on the theory of fuzzy (sub)sets in 1973 [START_REF] Kaufmann | Introduction à la Théorie des Sous-Ensembles Flous à l'usage des ingénieurs[END_REF]. It was translated into English two years later [START_REF] Kaufmann | Introduction to the Theory of Fuzzy Subsets[END_REF] 8 . The first 1973 volume was soon followed by three other ones [START_REF] Kaufmann | Introduction à la Théorie des Sous-Ensembles Flous[END_REF][START_REF] Kaufmann | Applications à la Classification et à la Reconnaissance des Formes, aux Automates et aux Systèmes[END_REF][START_REF] Kaufmann | Introduction à la Théorie des Sous-Ensembles Flous[END_REF], and by a book of exercises [START_REF] Kaufmann | Exercices avec Solutions sur la Théorie des Sous-Ensembles Flous[END_REF] (with Michel Cools and Thierry Dubois). Altogether, this series of five volumes mainly cover fuzzy set theoretic operations, fuzzy relations, and their applications to many fields: classification and pattern recognition, automata and systems, multicriteria decision, as well as linguistics, logic, topology, matroïds, etc. These books, and in particular the first one, had a great impact on the dissemination of fuzzy set theory in France. Continuing to write books on fuzzy logic-related topics, his strong interest for the topic never waned until the end of his life.

Let us quote the last paragraph of the conclusion of his first fuzzy set book [START_REF] Kaufmann | Introduction à la Théorie des Sous-Ensembles Flous à l'usage des ingénieurs[END_REF]:

Je voudrais exprimer un souhait très sincère. Je voudrais que mes lecteurs, initiés et intéressés par mon modeste travail, puissent aller plus loin, beaucoup plus loin, encore plus loin. Les sciences humaines ont besoin d'une mathématique appropriée à notre nature, à nos attitudes floues, à notre comportement nuancé, à nos dosages, à nos critères multiples. Si ce premier livre est suffisamment stimulant, de nombreux articles, concernant les aspects théoriques ou les applications, seront publiés par des lecteurs; des livres concurrents verront le jour. Tout ceci pour l'amélioration rapide de nos méthodes en vue d'aborder les sciences humaines." 9Beyond the fact that enthusiasm and generosity permeate this text, and the correctness of this prediction, it is also worth noticing that Kaufmann was considering that the applications of fuzzy set theory would be human-oriented sciences, while this is not so clear as of to-day. We have to remember that Kaufmann was writing this text at a time where information processing and artificial intelligence were still in infancy.

At the time when he got acquainted with fuzzy sets, Kaufmann was deeply interested in methods for helping creativeness [START_REF] Kaufmann | L'imagination artificielle -(Heuristique automatique). Revue franaise d'automatique, d'informatique et de recherche opérationnelle[END_REF], a topic on which he published a book later in 1979 [START_REF] Kaufmann | Modèles Mathématiques pour la Stimulation Inventive[END_REF]. So, it was one of the first areas where he considered applying fuzzy sets [START_REF] Collective | Art et Science: De la Créativité[END_REF][START_REF] Kaufmann | Stimulation inventive danss un dialogue homme-machine utilisant la méthode des morphologies et la théorie des sousensembles flous[END_REF][START_REF] Kaufmann | Introduction à la Théorie des Sous-Ensembles Flous[END_REF], for which he proposed a lattice and fuzzy relationbased approach, in the spirit of ideas and methods preiously advocated by Abraham Moles (1920Moles ( -1992)), an engineer by training, then a philosopher, working on the sociology and psychology of information and communication sciences [START_REF] Moles | La Création Scientifique[END_REF][START_REF] Moles | Sociodynamique de la Culture[END_REF][START_REF]Créativité et Méthodes d'innovation[END_REF] [74]. Kaufmann's approach to creativeness were also developed by his co-authors Michel Cools and Monique Peteau [START_REF] Cools | Un programme de stimulation inventive: STIM 5[END_REF].

Elie Sanchez -Claude Ponsard -Robert Féron

The first three main followers of Arnold Kaufmann in France in the mid-1970's are Elie Sanchez, Claude Ponsard, and Robert Féron .

Elie Sanchez (1944[START_REF] Seising | [END_REF] [12,[START_REF] Sanchez | An obituary[END_REF][START_REF] Seising | [END_REF] was the first in France, in 1974 in Marseilles, to defend a thesis on fuzzy set methods. His thesis is landmark piece of work on fuzzy relation equations, which contains important results on the solving of these equations [START_REF] Sanchez | Resolution of composite fuzzy relation equations[END_REF]. This research was motivated by an attempt at a mathematical formalization of medical diagnosis. It had a very strong influence on the development of fuzzy set methods worldwide.

Claude Ponsard (1927Ponsard ( -1990) [START_REF] Billot | Claude Ponsard (1927-1990): A biographical essay[END_REF][START_REF] Dubois | Obituary -Claude Ponsard[END_REF][START_REF] Fustier | Les apports des sous-ensembles flous à l'économie : les travaux des économistes dijonnais durant les années 80[END_REF], working in Dijon, started to propose in 1975 to apply fuzzy sets to various problems in economics [START_REF] Ponsard | Contribution à une théorie des espaces économiques imprécis[END_REF][START_REF] Ponsard | L'imprécision et son traitement en analyse économique[END_REF]. He then soon after led a small group of researchers on these questions, including Bernard Fustier [START_REF] Fustier | L'attraction des points de vente dans des espaces précis et imprécis[END_REF] and Régis Deloche [START_REF] Deloche | Théorie des sous-ensembles flous et classification en analyse économique spatiale[END_REF].

Robert Féron (b. 1921) [START_REF] Auray | Robert Féron: A pioneer in soft methods for probability and statistics[END_REF] is a statistician working in econometrics in Lyon. He was the first to properly provide a theoretical basis for the study of fuzzy random sets and to advocate their interest [START_REF] Féron | Ensembles aléatoires flous. Note CRAS, t[END_REF][START_REF] Féron | Economie d'échange aléatoire floue[END_REF][START_REF] Féron | Ensembles flous, ensembles aléatoires flous, et économie aléatoire floue[END_REF][START_REF] Féron | Ensembles flous attachés à un ensemble aléatoire flou Publications Econométriques[END_REF]. His writings, mostly in French, and mostly published in a journal having a limited circulation, would remain unfortunately largely ignored in the English American world. Let us also point out on the same kind of topic and published in the same place a paper by Robert Fortet and Mehri Kambouzia [START_REF] Fortet | Ensembles aléatoires et ensembles flous[END_REF].

We should also mention the two pioneering papers by Jean-Pierre Aubin (b. 1939) on game theory with fuzzy cores (the set of multistrategies that are not rejected by any coalition) published at that time [START_REF] Aubin | Coeur et valeur des jeux flous à paiements latéraux[END_REF][START_REF] Aubin | Coeur et valeur des jeux flous sans paiements latéraux[END_REF].

1974-1976: The pivotal years

From 1974-1976 on, the number of young French researchers interested in fuzzy sets started to increase (even if the topic was not very popular and remained highly controversial especially in France (many people were considering that it was not a "serious" topic to work on -partly because of the name -, and whose connection / difference with probability was unclear). Let us provide a list of persons in France who began to use fuzzy sets in their works at that time:

-Bernadette Bouchon, a member of the team headed by Claude-François Picard (1926Picard ( -1979) ) [START_REF] Picard | Théorie des questionnaires[END_REF] started working on fuzzy questionaries [START_REF] Bouchon | Du flou dans les questionnaires[END_REF],

-Jacques Brémont (1938Brémont ( -2014) ) defended his thesis on the use of fuzzy sets on speech recognition in 1975 [START_REF] Brémont | Contribution à la reconnaissance automatique de la parole par les sous-ensembles flous[END_REF] under the supervision of Michel Lamotte [START_REF] Brémont | Contribution à la reconnaissance automatique de la parole en temps réél par la considération des sous-ensembles flous[END_REF][START_REF] Mas | Commande vocale de processus industriels[END_REF]. Altogether with Gérard Hirsch (b. 1938) [START_REF] Benlahcen | Codage et minimization des fonctions floues dans une algèbre floue[END_REF] they later on formed an active research group on fuzzy set methods in Nancy for about two decades.

-The first French works on fuzzy systems were initiated by Pierre Vidal [START_REF] Malvache | Application des systèmes flous à la modélisation des phénomènes de prise de décision et d'appréhension des informations visuelles chez l'homme. Final report of the CNRS ATP[END_REF] in Lille in 1974, together with Noël Malvache (1943Malvache ( -2007) ) who then continued to work on fuzzy rule-based controllers with Didier Willaeys in Valenciennes [START_REF] Willaeys | Utilisation d'un référentiel de sous-ensembles flous[END_REF].

-the year 1975 sees the publication of the first fuzzy set papers by two French pure mathematicians, Daniel Ponasse [START_REF] Ponasse | Sur la notion de distance dans une structure floue régulière[END_REF] and S. Ribeyre [START_REF] Ribeyre | Etude des automorphismes de l'algèbre de De Morgan des parties floues d'un ensemble[END_REF]. The former, once back in France, launched a seminar on "Fuzzy Mathematics" in Lyon, which would become very productive in the late 1970's and the 1980's. This group included Achille Achache (b. 1934), Nicole Blanchard, Odile Botta, Josette and Jean-Louis Coulon, Marianne Delorme, and Christiane Dujet. Let us also mention Michel Eytan [START_REF] Eytan | Sémantique préordonnée des ensembles flous[END_REF] on this mathematical side.

Although the following people have been more briefly involved with fuzzy sets, one may still mention:

-in automation of production processes, the thesis of Moncef Ben Salem (1953Salem ( -2015) ) [START_REF] Salem | Sur l'extension de la théorie des sous-ensembles flous à l'automatique industrielle. Mise au point d'une nouvelle méthode d'étude des gammes d'usinage[END_REF] where a fuzzy multicriteria automatic decision-making procedure is proposed for determining the sequencing of operations accomplished by a machine tool. Later, Ben Salem became minister of Higher Education and Scientific Research (2011-2014), after the Tunisian revolution. Lucas Pun [START_REF] Pun | Use of fuzzy formalism in problems with various degree of subjectivity[END_REF] was one of the very first in France to foresee the potential interest of fuzzy sets in the modeling of production processes.

-Jean-Marc Adamo (b. 1943) [START_REF] Adamo | Towards the introduction of fuzzy concepts in dynamic modeling[END_REF] started working in the second half of the 1970's for some years on dynamical systems and then on fuzzy programming languages.

-Jean-Philippe Massonie [START_REF] Massonie | L'utilisation des sous-ensembles flous en géographie[END_REF] in Besançon was the first in France to foresee the potential interest of fuzzy sets in geographical modeling, thus initiating a line of research that still exists in France.

What is more unexpected is that fuzzy sets were also a source of inspiration in the French avant-garde literature. The French novelist Claude Ollier [START_REF] Ollier | Fuzzy Sets[END_REF], a writer close to the "Nouveau Roman" movement, seems to have met Arnold Kaufmann in September 1970, at a meeting about creativeness in art and science [START_REF] Collective | Art et Science: De la Créativité[END_REF], where Kaufmann already spoke about fuzzy sets. In this French novel with an English title "Fuzzy sets", the author plays with the roles of the protagonists and the reader in the story, as well as with the display of the text on the pages. The novel was reprinted with a slightly less exotic page display two decades later [START_REF] Ollier | Fuzzy Sets[END_REF]. Let us mention a more classical writer, Jacques Laurent, who published a novel also with the title "Les sous-ensembles flous" (this time in French) a bit later in 1981 [START_REF] Laurent | Les Sous-Ensembles Flous[END_REF]. In this book, the fuzzy set idea applies at several levels to the links between the characters and the forces that drive them.

Lastly, it is in 1976 that the authors of this note produced their first (handwritten !) research report of [START_REF] Dubois | Le flou[END_REF] (now indexed by Google Books). This was mainly a survey and a status report. Our first published contributions only appeared one year later [83, 25, ?] This note is an attempt at offering a short overview of the first years of research in France regarding fuzzy sets and their applications. Only references from mid-seventies and before have been reported, without mentioning further developments of the works of the authors cited. In fact, some authors have encountered fuzzy sets very briefly in their research in this time period, while others have continued to contribute to fuzzy sets for several decades.

As shown by this brief overview, fuzzy set research in France (see [11, ?] for general overviews), starts in the years 1973-1976, and immediately deals with very different issues. They are led by researchers relatively isolated from one another, who often face suspicion, negative critique, and sometimes disparagement and bashing from their academic colleagues. Nevertheless, those times were more open-minded than the present period that seems to be under the tyranny and normalization of citation rates and impact factors! It is also worth noticing that the first works rely mainly on fuzzy set operations and on fuzzy relations, and that many important notions have no role in these works, even if they already exist as the extension principle [START_REF] Zadeh | Fuzzy sets[END_REF], or the notions of fuzzy measures and fuzzy integrals in the sense of Sugeno [START_REF] Sugeno | Theory of Fuzzy Integrals and its Applications[END_REF] 10 . It is a matter of facts that some crucial developments would only appear a bit later, such as possibility theory [START_REF] Zadeh | Fuzzy sets as a basis for a theory of possibility[END_REF], or the linkage between fuzzy set connectives and triangular norms, originally introduced in the study of probabilistic metric spaces, whose father was precisely Karl Menger, the man who first used the phrase "ensemble flou"!

In English: "We shall call such a function a fuzzy set and we shall interpret Π F (x) as the probability that x belongs to this set. If Π F only takes the values 1 and 0, it is essentially a subset of U in the classical sense and we shall speak of crisp set."

Reference[START_REF] Menger | Ensembles flous et fonctions aléatoires[END_REF].

R. Bellman, R. Kalaba, L. Zadeh. Abstraction and pattern classification. J. of Mathematical Analysis and Applications, 13 (1), 1-7, January 1966.

In English: "In view of a theory of non additive set functions, one defines the class of the subsets of separated spaces, generated from compacts by denumerable unions or intersections and by continuous mappings."

the use of this word , which means "clouds" reminds us that at the beginning Zadeh was hesitating between the words "fuzzy" and "cloudy": Indeed, he wrote in 1962: "we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions." in[START_REF] Zadeh | From circuit theory to system theory[END_REF]

This list by no means claims to exhaustiveness!

This more theoretical book, first written in Romanian in 1974[START_REF] Negoita | Multimi vagi si aplicatiile lor. (Ensembles flous et leurs applications)[END_REF] would appear in English also in 1975[START_REF] Negoita | Application of Fuzzy Sets to Systems Analysis[END_REF].

"I would like to express a very sincere wish. I would like that my readers, taught and interested by my modest work, go farther, much farther and farther. Human-oriented sciences need a kind of mathematics that fits our nature, our fuzzy attitudes, our nuanced behavior, our balanced judgments, our multiple criteria. If this first book is sufficiently stimulating, many articles, dealing with theoretical or practical aspects, will be published by my readers; concurrent monographs will appear. All this, for the fast improvement of our methods for coping with human-oriented sciences."

Interestingly enough, Michio Sugeno spent the academic year 1976-1977 in Toulouse, at the LAAS laboratory, in the research group of José Aguilar Martin[START_REF] Seif | Multi-group classification using fuzzy correlation[END_REF] and Gérald Banon[START_REF] Banon | Distinction entre plusieurs sous-ensembles de mesures floues[END_REF]. The authors of this note were lucky enough to meet Sugeno and learn about his research by the end of his stay in Toulouse.