We compare two approaches to probability on systems of fuzzy sets—measures on tribes as introduced by Butnariu and Klement [3] and measures on MV-algebras with product studied by Riečan and Mundici [21]. We show that these two approaches overlap significantly and they confirm the original proposal of probability measure on fuzzy sets by Zadeh [24].

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by [Emamjomeh-Zadeh et al., STOC, 2016] to the problem of detecting a target in an arbitrary graph. Similarly to the classical case in the path, the algorithm of Emamjom...

This special issue encompasses six papers devoted to the recent advancements in the field of fuzzy sets. The seed of the current issue were some of the presentations made in three special sessions organized by the guest editors at the Nineth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2002) that was held in Annecy, France, Ju...

The TOPSIS process is one of the most comprehensive systems designed for decision making with multiple criteria, since this technique enables formulation of the problem as decision matrix, as well as the possibility of considering different quantitative and qualitative criteria in the problem. Fuzzy TOPSIS methods have been introduced to make fundamental decisions that make decisions decisions ...

An issue that is of considerable interest in distributed systems is the selection of a solution acceptable to a collection agents when each agent has their own preferences among a set of alternative possible solutions. Recently Rosenchein and Zlotkin [1] have presented a comprehensive work discussing this issue. The process of finding such a solution can be seen as a kind of negotiation amongst...

Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...

Type-2 fuzzy sets have come to play an increasingly important role in both applications and in the general theory of fuzzy sets. The basis of type-2 fuzzy sets is a certain algebra of truth values, as set forth by Zadeh. This paper is a survey of results about this algebra, along with some new material.

This note provides conditions under which Zadeh extension of a map between L -topological spaces preserves semicontinuity and continuity of functions with values in the L-unit interval. Invariance of complete L-regularity under continuous open–closed surjections is established among others. © 2012 Elsevier B.V. All rights reserved.

Granular computing(GrC) is a recent label, roughly speaking, jointly coined by Lin and Zadeh in 1996 to denote an emgering technolgy that is based on the computing/mathematical theory of an ancient concept of granulation. In this paper, we present the ”final” GrC model that simplify the earlier version.