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: (...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

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...