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Generalized convexities related to aggregation operators of fuzzy sets

Susana Díaz; Esteban Induráin; Vladimír Janiš; Juan Vicente Llinares; Susana Montes — 2017

Kybernetika

We analyze the existence of fuzzy sets of a universe that are convex with respect to certain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping $F : [0, 1] \times [0, 1] \to [0, 1]$ , a fuzzy subset, say $X$ , of the real line is said to be $F$ -convex if for any $x, y, z \in ℝ$ such that $x \leq y \leq z$ , it holds that $μ_{X} (y) \geq F (μ_{X} (x), μ_{X} (z))$ , where $μ_{X} : ℝ \to [0, 1]$ stands here for the membership function...

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