Let X be a compact metric space and let f : X → X be continuous. It is well known that a given discrete dynamical system (X, f) induces a map Φ on the space F(X) of fuzzy sets. In this paper we study relations between sizes of topological entropies of a given crisp dynamical system (X, f) and its fuzzy counterpart (F(X),Φ). Among another things, we present a constructive proof of the fact that ...

Any strict partial order R on a nonempty set X defines a function θR which associates to each strict partial order S ⊆ R on X the strict partial order θR(S) = R ◦ S on X. Owing to the strong relationships between Alexandroff TD derivative operators and strict partial orders, this paper firstly calls forth the links between the CantorBendixson ranks of Alexandroff TD topological spaces and the g...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy almost weakly generalized closed mappings and intuitionistic fuzzy almost weakly generalized open mappings in intuitionistic fuzzy topological space. Some of their properties are explored.

In this paper the concept of interval valued intuitionistic fuzzy soft topological space(IVIFS topological space) together with interval valued intuitionistic fuzzy soft open sets(IVIFS open sets) and interval valued intuitionistic fuzzy soft closed sets(IVIFS closed sets) are introduced. We define neighbourhood of an IVIFS set, interior IVIFS set, interior of an IVIFS set, exterior IVIFS set, ...

We introduce r -fuzzy strongly preopen and r -fuzzy strongly preclosed sets in fuzzy topological space in view of the definition of Šostak (1985). We investigate some properties of them. Moreover, the concepts of fuzzy SP-continuous, fuzzy SP-irresolute continuous, fuzzy SP-irresolute open (closed) mappings, and a fuzzy SP-irresolute homeomorphism are introduced and studied. Some of their chara...

In this paper we introduce the gradation of separation axioms ST 0 , RT 0 in an intuitionistic fuzzy topological space in the sense of Mondal and Samanta [7]. Using these concepts we have introduced and studied α-and α *-RT 0 intuitionistic fuzzy topological spaces.

We introduce the notion of (r,s)-connected sets in intuitionistic fuzzy topological spaces and investigate some properties of them. In particular, we show that every (r,s)-component in an intuitionistic fuzzy topological space is (r,s)-component in the stratification of it.

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A...