The concept of a fuzzy set was introduced by Zadeh [13], and later Chang [3] defined fuzzy topological spaces. These spaces and their generalizations are later studied by several authors, one of which, developed by Šostak [11, 12], used the idea of degree of openness. This type of generalization of fuzzy topological spaces was later rephrased by Chattopadhyay et al. [4], and by Ramadan [10]. In...

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some ...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S. Keywords—Semigroup, Regular(intra-regular) semigroup, In...

Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of...

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constr...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. Using the notion of intuitionistic fuzzy sets, Çoker [5] introduced the notion of intuitionistic fuzzy topological spaces. In this paper, we define the notion of intuitionistic fuzzy semiopen (r...