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On idempotent n-ary uninorms Devillet, Jimmy ; ; Marichal, Jean-Luc in Torra, Vicenç; Narukawa, Yasuo; Pasi, Gabriella (Eds.) et al Modeling Decisions for Artifical Intelligence (2019, July 24) In this paper we describe the class of idempotent n-ary uninorms on a given chain.When the chain is finite, we axiomatize the latter class by means of the following conditions: associativity ... [more ▼] In this paper we describe the class of idempotent n-ary uninorms on a given chain.When the chain is finite, we axiomatize the latter class by means of the following conditions: associativity, quasitriviality, symmetry, and nondecreasing monotonicity. Also, we show that associativity can be replaced with bisymmetry in this new axiomatization. [less ▲] Detailed reference viewed: 50 (7 UL)Characterizations of biselective operations Devillet, Jimmy ; in Acta Mathematica Hungarica (2019), 157(2), 387-407 Let X be a nonempty set and let i,j in {1,2,3,4}. We say that a binary operation F:X^2 -> X is (i,j)-selective if F(F(x_1,x_2),F(x_3,x_4)) = F(x_i,x_j), for all x_1,x_2,x_3,x_4 in X. In this paper we ... [more ▼] Let X be a nonempty set and let i,j in {1,2,3,4}. We say that a binary operation F:X^2 -> X is (i,j)-selective if F(F(x_1,x_2),F(x_3,x_4)) = F(x_i,x_j), for all x_1,x_2,x_3,x_4 in X. In this paper we provide characterizations of the class of (i,j)-selective operations. We also investigate some subclasses by adding algebraic properties such as associativity or bisymmetry. [less ▲] Detailed reference viewed: 89 (25 UL)Characterizations of idempotent n-ary uninorms Devillet, Jimmy ; ; Marichal, Jean-Luc in 38th Linz Seminar on Fuzzy Set Theory (2019, February 05) In this paper we provide a characterization of the class of idempotent n-ary uninorms on a given chain. When the chain is finite, we also provide anaxiomatic characterization of the latter class by means ... [more ▼] In this paper we provide a characterization of the class of idempotent n-ary uninorms on a given chain. When the chain is finite, we also provide anaxiomatic characterization of the latter class by means of four conditions only: associativity, quasitriviality, symmetry, and nondecreasing monotonicity. In particular, we show that associativity can be replaced with bisymmetry in this axiomatization. [less ▲] Detailed reference viewed: 77 (18 UL)On the best constants associated with n-distances ; Marichal, Jean-Luc E-print/Working paper (2019) We pursue the investigation of the concept of n-distance, an n-variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and Teheux. We especially focus ... [more ▼] We pursue the investigation of the concept of n-distance, an n-variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and Teheux. We especially focus on the challenging problem of computing the best constant associated with a given n-distance. In particular, we define and investigate the best constants related to partial simplex inequalities. We also introduce and discuss some subclasses of n-distances defined by considering some properties. Finally, we discuss an interesting link between the concepts of n-distance and multidistance. [less ▲] Detailed reference viewed: 38 (13 UL)An n-ary generalization of the concept of distance ; Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2018, July 03) Detailed reference viewed: 55 (5 UL) |
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