Aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving various kinds of convexity. We focus on aggregation functions for intuitionistic fuzzy sets. These functions correspond to simultaneous separate aggregations of the membership as well as of the nonmembership indicators. It is performed by means of the so-called representable functions. Sufficient and necess...

The construction of distributions with given marginals has been a problem of interest to statisticians for many years. Today, in view of Sklar’s theorem [25, 26], this problem can be reduced to the construction of a copula. Copulas are a special type of aggregation functions, and nowadays are of interest in fuzzy set theory [5, 6, 12, 14, 16]. Nelsen [22] summarizes different methods of constru...

Throughout this paper, our  main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical  mod...

in this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. thena relation between totally fuzzy bounded sets and n-compactness is discussed.finally, a geometric characterization for fuzzy totally bounded sets in i- topologicalvector spaces is derived.

This paper is devoted to propose triangular fuzzy number neutrosophic sets by combining triangular fuzzy numbers with single valued neutrosophic set and define some of its operational rules. Then, triangular fuzzy number neutrosophic weighted arithmetic averaging operator and triangular fuzzy number neutrosophic weighted geometric averaging operator are defined to aggregate triangular fuzzy num...

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

The fuzzy logic operators are used to decide the following multicriteria decision-making problem. A finite set of alternatives is evaluated by a set of fuzzy criteria, i.e., fuzzy relations, which may be either fuzzy preference, or similarity, or likeness relations. The problem is to construct an evaluation procedure to compare the set of alternatives according to the whole set of criteria, i.e...