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Cut properties of resemblance

The resemblance relation is used to reflect some real life situations for which a fuzzy equivalence is not suitable. We study the properties of cuts for such relations. In the case of a resemblance on a real line E we show that it determines a special family of crisp functions closely connected to its cut relations. Conversely, we present conditions which should be satisfied by a collection of real functions in E in order that this collection determines a resemblance relation.

Poset-valued preference relations

In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives...

Generalized convexities related to aggregation operators of fuzzy sets

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 ] × [ 0 , 1 ] [ 0 , 1 ] , a fuzzy subset, say X , of the real line is said to be F -convex if for any x , y , z such that x y z , it holds that μ X ( y ) F ( μ X ( x ) , μ X ( z ) ) , where μ X : [ 0 , 1 ] stands here for the membership function...

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