Our interest in this paper is to define and study the concept of a fuzzy hypergroup, which depends on the concept of a fuzzy space. Indeed, the paper is a continuation of ideas presented by Davvaz [Fuzzy Sets and Systems, 101 (1999) 191-195]. A relation between a fuzzy hypergroup based on a fuzzy space and a fuzzy hypergroup in the sense of Davvaz is obtained 2010 AMS Classification: 20N20

In 2011, Mallozzi et al. [Fuzzy Sets and Systems 165(2011) 98105] introduced a core-like concept (called F-core) and a balanced-like condition for games in which the worth of any coalition is given by means of a fuzzy interval. They proved that a balanced-like condition is necessary but not sufficient enough to guarantee the F-core to be non-empty. In this paper, we study deeply on this problem...

This paper is an investigation of the automorphisms of the algebra of truth values of type-2 fuzzy sets. This algebra contains isomorphic copies of the truth value algebras of type-1 and of interval-valued fuzzy sets. It is shown that these subalgebras are characteristic; that is, are carried onto themselves by automorphisms of the containing algebra of truth values of fuzzy sets. Some other re...

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also...

Welcome to the Journal of Intelligent and Fuzzy Systems’s special issue for “FUZZYSS’2011: 2nd International Fuzzy Systems Symposium”. Since its introduction by Prof. Dr. Lotfi A. Zadeh fuzzy logic, fuzzy sets and systems have been applied to various problems in many diverse areas. As everything try to evolve towards better states, the fuzzy theory and its applications are also evolving to mode...

In this paper we associate the three concepts of language, thinking, and meaning with Fuzzy Sets and Systems and Fuzzy Logic. We present some developments in 20 th century history of science and of humanities that show deep links between these concepts and we give a proposal for a fuzzy theoretical interpretation of what is meaning.

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ~ on the set I of all fuzzy implications they obtained, for the first time, a monoid structure (I,~) on the set I. Some algebraic aspects of (I,~) had already been explored and hitherto unknown representation results for the Yager’s fa...

This paper is a continuation of the first part of our study on type 〈1, 1〉 fuzzy quantifiers determined by fuzzy measures, in which the basic notions and examples were introduced. Here, we study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers determined by pairs of functionals (S, φ) and their special cases, e.g., fuzzy quantifiers defined by fuzzy measu...

The shapes of terms used in fuzzy systems have adopted several ‘conventions’. Terms are almost invariably normalised (having a maximum membership value of 1), convex (having a single maximum or plateau maxima) and distinct (being restricted in their degree of overlap: often expressed as some variation on the concept that all membership values at any point in the universe of discourse sum to 1 a...