The aim of this paper is to study the concept of -induced L-fuzzy topological spaces. Some properties of the functions (namely Scott-continuous function) are studied. The Scott-continuous functions turn out to be the natural tool for studying the -induced L-fuzzy topological space. We also discuss the connections between some separations, countability and covering properties of an ordinary topo...

Topological relations are one of the most fundamental properties between spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalise the topological relations between fuzzy regions needs more investigation. The paper starts from introduction of boundaries defined in the fuzzy topological space. By use of a definition formally equi...

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...

Introduction § 0. Preliminaries: fuzzy sets 125 § 1. Fuzzy topological spaces: the basic categories of fuzzy topology 127 § 2. Fundamental interrelations between the category Top of topological 135 spaces and the categories of fuzzy topology § 3. Local structure of fuzzy topological spaces 138 § 4. Convergence structures in fuzzy spaces 140 § 5. Separation in fuzzy spaces 143 § 6. Normality and...

In this paper we have introduced and studied 2α,β-connectedness and Dconnectedness in an intuitionistic fuzzy topological space as extensions of 2αconnectedness and D-connectedness respectively in a fuzzy topological space (given by Lowen and Srivastava) and proved some basic results related to it. We have also introduced some other type of connectedness in an intuitionistic fuzzy topological s...

In this article on fuzzy topological spaces we studied and the further investigated different kind of continues mappings in fuzzy topological space. In this article fuzzy sets have been defined and use of fuzzy numbers in daily life. In this article we have investigated how the fuzzy topological spaces have been defined by different authors and what is its future scope.

The aim of this paper is to extend the notion of topological entropy for fuzzy semidynamical systems created by a self-map on a fuzzy metric space. We show that if a metric space has two uniformly equivalent metrics, then fuzzy entropy is a constant up to these two metrics. We present a method to construct chaotic fuzzy semidynamical systems with arbitrary large fuzzy entropy. We also prove tha...