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 References of "Couceiro, Miguel"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 31 1 2     Reducibility of n-ary semigroups: from quasitriviality towards idempotencyCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc et alin Beiträge zur Algebra und Geometrie (2022), 63(1), 149-166Let $X$ be a nonempty set. Denote by $\mathcal{F}^n_k$ the class of associative operations $F\colon X^n\to X$ satisfying the condition $F(x_1,\ldots,x_n)\in\{x_1,\ldots,x_n\}$ whenever at least $k$ of the ... [more ▼]Let $X$ be a nonempty set. Denote by $\mathcal{F}^n_k$ the class of associative operations $F\colon X^n\to X$ satisfying the condition $F(x_1,\ldots,x_n)\in\{x_1,\ldots,x_n\}$ whenever at least $k$ of the elements $x_1,\ldots,x_n$ are equal to each other. The elements of $\mathcal{F}^n_1$ are said to be quasitrivial and those of $\mathcal{F}^n_n$ are said to be idempotent. We show that $\mathcal{F}^n_1=\cdots =\mathcal{F}^n_{n-2}\subseteq\mathcal{F}^n_{n-1}\subseteq\mathcal{F}^n_n$ and we give conditions on the set $X$ for the last inclusions to be strict. The class $\mathcal{F}^n_1$ was recently characterized by Couceiro and Devillet \cite{CouDev}, who showed that its elements are reducible to binary associative operations. However, some elements of $\mathcal{F}^n_n$ are not reducible. In this paper, we characterize the class $\mathcal{F}^n_{n-1}\setminus\mathcal{F}^n_1$ and show that its elements are reducible. We give a full description of the corresponding reductions and show how each of them is built from a quasitrivial semigroup and an Abelian group whose exponent divides $n-1$. [less ▲]Detailed reference viewed: 177 (32 UL) Every quasitrivial n-ary semigroup is reducible to a semigroupCouceiro, Miguel; Devillet, Jimmy in Algebra Universalis (2019), 80(4), We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in ... [more ▼]We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary semigroups. We also explicitly determine the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences. [less ▲]Detailed reference viewed: 286 (62 UL) Characterizations and enumerations of classes of quasitrivial n-ary semigroupsDevillet, Jimmy ; Couceiro, MiguelScientific Conference (2019, June 23)Detailed reference viewed: 113 (8 UL) Quasitrivial semigroups: characterizations and enumerationsCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc in Semigroup Forum (2019), 98(3), 472498We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order ... [more ▼]We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences. [less ▲]Detailed reference viewed: 364 (107 UL) Single-peakedness in aggregation function theoryDevillet, Jimmy ; Couceiro, Miguel; Marichal, Jean-Luc Presentation (2019, May 14)Due to their great importance in data fusion, aggregation functions have been extensively investigated for a few decades. Among these functions, fuzzy connectives (such as uninorms) play an important role ... [more ▼]Due to their great importance in data fusion, aggregation functions have been extensively investigated for a few decades. Among these functions, fuzzy connectives (such as uninorms) play an important role in fuzzy logic. We establish a remarkable connection between a family of associative aggregation functions, which includes the class of idempotent uninorms, and the concepts of single-peakedness and single-plateaudness, introduced in social choice theory by D. Black. Finally, we enumerate those orders when the underlying set is finite. [less ▲]Detailed reference viewed: 110 (10 UL) Associative and quasitrivial operations on finite sets: characterizations and enumerationCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc Scientific Conference (2018, July 02)We investigate the class of binary associative and quasitrivial operations on a given finite set. Here the quasitriviality property (also known as conservativeness) means that the operation always outputs ... [more ▼]We investigate the class of binary associative and quasitrivial operations on a given finite set. Here the quasitriviality property (also known as conservativeness) means that the operation always outputs one of its input values. We also examine the special situations where the operations are commutative and nondecreasing, in which cases the operations reduce to discrete uninorms (which are discrete fuzzy connectives playing an important role in fuzzy logic). Interestingly, associative and quasitrivial operations that are nondecreasing are characterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black. We also address and solve a number of enumeration issues: we count the number of binary associative and quasitrivial operations on a given finite set as well as the number of those operations that are commutative and/or nondecreasing. [less ▲]Detailed reference viewed: 91 (5 UL) Clones of pivotally decomposable operationsCouceiro, Miguel; Teheux, Bruno Scientific Conference (2018, June)We investigate the clones of operations that are pivotally decomposable.Detailed reference viewed: 56 (3 UL) Characterizations of idempotent discrete uninormsCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc in Fuzzy Sets and Systems (2018), 334In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an ... [more ▼]In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open questions for further research. [less ▲]Detailed reference viewed: 280 (54 UL) Pivotal decomposition schemes inducing clones of operationsCouceiro, Miguel; Teheux, Bruno in Beitraege zur Algebra und Geometrie = Contributions to Algebra and Geometry (2018), 59(1), 25-40We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of ... [more ▼]We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations are clones, and show that under certain assumptions these conditions are also necessary. In the latter case, the pivotal operation together with the constant operations generate the corresponding clone. [less ▲]Detailed reference viewed: 126 (22 UL) Associative and quasitrivial operations on finite sets (invited lecture)Marichal, Jean-Luc ; Couceiro, Miguel; Devillet, Jimmy Scientific Conference (2017, November 10)Detailed reference viewed: 87 (13 UL) On quasitrivial and associative operationsDevillet, Jimmy ; Couceiro, Miguel; Marichal, Jean-Luc Presentation (2017, October 25)Detailed reference viewed: 81 (13 UL) Enumerating quasitrivial semigroupsDevillet, Jimmy ; Couceiro, Miguel; Marichal, Jean-Luc Presentation (2017, October 03)We investigate the class of binary associative and quasitrivial operations on a given finite set. Here quasitriviality (also known as conserva-tiveness) means that the operation always outputs one of its ... [more ▼]We investigate the class of binary associative and quasitrivial operations on a given finite set. Here quasitriviality (also known as conserva-tiveness) means that the operation always outputs one of its input values. We also examine the special situations where the operations are commutative and nondecreasing. In the latter case, these operations reduce to discrete uninorms, which are discrete fuzzy connectives that play an important role in fuzzy logic. As we will see nondecreasing, associative and quasitrivial operations are chara-cterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black. This will enable visual interpretaions of the above mentioned algebraic properties. Motivated by these results, we will also address a number of counting issues: we enumerate all binary associative and quasitrivial operations on a given finite set as well as of those operations that are commutative, are nondecreasing, have neutral and/or annihilator elements. As we will see, these considerations lead to several, previously unknown, integer sequences. [less ▲]Detailed reference viewed: 93 (16 UL) Sur les uninormes discrètes idempotentesCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc in Couceiro, Miguel; Devillet, Jimmy; Marichal, Jean-Luc (Eds.) LFA 2017 - Rencontres francophones sur la logique floue et ses applications (2017, October)In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values ... [more ▼]In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element. [less ▲]Detailed reference viewed: 86 (8 UL) On conservative and associative operations on finite chainsDevillet, Jimmy ; Couceiro, Miguel; Marichal, Jean-Luc Scientific Conference (2017, June 16)See attached fileDetailed reference viewed: 100 (25 UL) On idempotent discrete uninormsCouceiro, Miguel; Devillet, Jimmy ; Marichal, Jean-Luc in De Baets, Bernard; Torra, Vicenç; Mesiar, Radko (Eds.) Aggregation Functions in Theory and in Practice (2017, June)In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values ... [more ▼]In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element. [less ▲]Detailed reference viewed: 211 (39 UL) Relaxations of associativity and preassociativity for variadic functionsCouceiro, Miguel; Marichal, Jean-Luc ; Teheux, Bruno in Fuzzy Sets and Systems (2016), 299In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized ... [more ▼]In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research. [less ▲]Detailed reference viewed: 206 (24 UL) Conservative median algebras and semilatticesCouceiro, Miguel; Marichal, Jean-Luc ; Teheux, Bruno in Order: A Journal on the Theory of Ordered Sets and its Applications (2016), 33(1), 121-132We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median ... [more ▼]We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains. [less ▲]Detailed reference viewed: 202 (13 UL) Agrégation des valeurs médianes et fonctions compatibles pour la comparaisonCouceiro, Miguel; Marichal, Jean-Luc ; Teheux, Bruno in Lefèvre, Erice; Hadjali, Allel (Eds.) Rencontres francophones sur la logique floue et ses applications 2015 (2015, November)Nous caractérisons les fonctions d'agrégation qui préservent la valeur médiane dans le cas où l'opération médiane est conservative. Nous commençons par rappeler les notions d'algèbre et de demi-treillis ... [more ▼]Nous caractérisons les fonctions d'agrégation qui préservent la valeur médiane dans le cas où l'opération médiane est conservative. Nous commençons par rappeler les notions d'algèbre et de demi-treillis médian en les introduisant à partir de la notion de valeur médiane sur les réels. Nous obtenons également une double caractérisation des algèbres médianes conservatives en termes de sous-structures interdites et de représentations par des chaînes [less ▲]Detailed reference viewed: 113 (11 UL) Median Preserving Aggregation FunctionsCouceiro, Miguel; Marichal, Jean-Luc ; Teheux, Bruno in Baczyński, Michal; De Baets, Bernard; Mesiar, Radko (Eds.) Proceedings of the 8th Int. Summer School on Aggregation Operators (2015, July)A median algebra is a ternary algebra that satisfies every equation satisfied by the median terms of distributive lattices. We present a characterization theorem for aggregation functions over ... [more ▼]A median algebra is a ternary algebra that satisfies every equation satisfied by the median terms of distributive lattices. We present a characterization theorem for aggregation functions over conservative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures and by providing their representation as chains. [less ▲]Detailed reference viewed: 98 (3 UL) Clones of Pivotally Decomposable FunctionsCouceiro, Miguel; Teheux, Bruno in Multiple-Valued Logic (ISMVL), 2015 IEEE International Symposium on (2015, May 20)This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set and clones on the same set.Detailed reference viewed: 118 (4 UL) 1 2