The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on...

In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,i] X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule "lira" which to any prefilter on X assigns, a function lira E [0,i] X. We give necessary and sufficient conditions for the function lim in order that it can be derived f...

The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties proper sets. presentation the shows a thorough discussion on different alternatives that could be taken define desired systems. These plausible are discarded if they proven impossible in bijective correspondence operators. Finally, definition system established and one-to-one relation operator...

In the present paper we introduce the topological structure of fuzzy soft sets and fuzzy soft continuity of fuzzy soft mappings. We show that a fuzzy soft topological space gives a parametrized family of fuzzy topological spaces. Furthermore, with the help of an example it is shown that the constant mapping is not continuous in general. Then the notions of fuzzy soft closure and interior are in...

The goal of this paper is to investigate the certain properties bipolar fuzzy supra preopen sets (BF set). We introduce and study concepts pre-interior pre-interior) pre-closure pre-closure) operators. Furthermore, we define new type continuous mapping based on BF sets.

Based on fuzzy gp*-closed sets and gp*-open sets, in this paper we have introduced gp*- neighborhoods, gp*-Interior gp*-Closure. Also investigated some of their elementary properties discuss important theorems

In this paper X, Y denote non empty sets. Let X be a non empty set. Observe that every membership function of X is real-yielding. Let f , g be real-yielding functions. The predicate f ⊑ g is defined by: (Def. 1) dom f ⊆ dom g and for every set x such that x ∈ dom f holds f(x) ¬ g(x). Let X be a non empty set and let f , g be membership functions of X. Let us observe that f ⊑ g if and only if: (...

Properties of sup-∗ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup-∗ powers of fuzzy relations under diverse assumptions about ∗ operation. At first, we remind fundamental properties of sup-∗ composition. Then, ...

Principal methods in nonhierarchical and hierarchical fuzzy clustering are overviewed. In particular, the method of fuzzy c-means is focused upon and recent algorithms in fuzzy c-means are described. It is shown that the concept of regularization plays an important role in the fuzzy c-means. Classification functions induced from fuzzy clustering are discussed and variations of the standard fuzz...