we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the multiplicative consistency of the hesitant fuzzy preference relation. First of all, we explore some properties of the hesitant fuzzy preference relation and develop some new ag...

This paper is a survey of fuzzy set theory applied in cluster analysis. These fuzzy clustering algorithms have been widely studied and applied in a variety of substantive areas. They also become the major techniques in cluster analysis. In this paper, we give a survey of fuzzy clustering in three categories. The first category is the fuzzy clustering based on fuzzy relation. The second one is t...

We introduce a fuzzy implication stemming from a fuzzy lattice inclusion measure. We study “reasonable axioms” and properties of the aforementioned fuzzy implication, which (properties) are typicaly required in the literature and could be important in certain applications.

In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC)L or (TC)R axioms and the L-relations induced by two L-fuzzy topologi...

The paper investigates fuzzy relations on a finite domain in the cutworthy framework, dealing with a new property coming from the information theory. If the domain of a relation is considered to be a table, then a rectangular subset of the domain whose values under this relation are greater than the values of all neighboring fields is called an island. Consequently, the so called rectangular fu...

A T-fuzzy equivalence relation is a fuzzy binary relation on a set X which is reflexive, symmetric and T-transitive for a t-norm T. Recently, Mesiar et al. [R. Mesiar, B. Reusch, H. Thiele, Fuzzy equivalence relations and fuzzy partitions, J. Multi-Valued Logic Soft Comput. 12 (2006) 167–181] have generalised the t-norm T to any general conjunctor C and investigated the minimal assumptions requ...

A new concept of the inclusion measure for intuitionistic fuzzy sets is proposed by the axiomatic definition. Also, the distance measures, similarity measures and information entropy are recalled and summarized. Most of important, some relationships among distance measure, information entropy, and inclusion measure of IFSs are then investigated. Finally, we obtain some important theorems by whi...

New adaptive search methods based on multiresolution analysis and wavelet theory are introduced and discussed within the framework of Markov theory. These stochastic search methods are suited to problems for which good solutions tend to cluster within the search space. Multiresolution search methods are extended to searches with memory. The introduction of a memory allows an easy inclusion of l...

The paper deals in a preliminary way with the problem of the selection of a unique fuzzy preference relation from the set of fuzzy preference relations. A direct algorithm of possibilistic clustering is the basis of the method of fuzzy preference relation discriminating. A method of decision-making based on a fuzzy preference relation is described and basic concepts of the heuristic method of p...