Group Intuitionistic Fuzzy Topological Spaces

The notion of intuitionistic fuzzy set was introduced by K.T. Atanassov as a generalization of the notion of fuzzy set. Intuitionistic fuzzy topological spaces were introduced by D. Coker and studied by many eminent authors like F. Gallego Lupianez, K. Hur, J. H. Kim and J. H. Ryou. R. Biswas applied the notion of intuitionistic fuzzy set to algebra and introduced intuitionistic fuzzy subgroup of a group. In this paper, we will study intuitionistic fuzzy topology by involving the algebraic structure on it and introduce the notion of group intuitionistic fuzzy topological spaces. We will examine many properties of these spaces and obtain several results. Keywords: Intuitionistic fuzzy topological space (IFTS), intuitionistic fuzzy subgroup (IFSG), group intuitionistic fuzzy topological space (GIFTS), intuitionistic fuzzy point (IFP).

Generalization of Tichonov and Hausdorff ‎Separation Axiomes in Intuitionistic Fuzzy ‎Special Topological Spaces

هدفنا من هذا البحث هو تعميم تعريف بديهية فصل تيكنوف وبديهية الفصل هاوسدورف  في الفضاءات التبولوجية  الحدسية الخاصة ودراسة العلاقات بين هذه الفضاءات مع الفضاءات التبولوجية الحدسية الخاصة  من نوع  (X, τ2) و (X, τ1) من جهة والفضاءات التبولوجية الحدسية الخاصة  من نوع (X, τ 0,2)و  (X, τ0,1)  من جهة اخرىOur goal in this paper is to give definitions of generalized of Tichonov and Hausdorff separation axioms in intuitionistic fuzzy special topological spaces, and study relationships between these spaces with the intuitionistic special topological spaces (X, τ0,1) and (X, τ 0,2) on one hand and intuitionistic fuzzy special topological spaces (X, τ1) and (X, τ2) on the other han

A study on fuzzy connectedness and fuzzy continuity in fuzyy topological spaces

Fuzzy connectedness and fuzzy continuity are important concepts in the field of fuzzy mathematics, and have been studied in various types of fuzzy spaces. In this review paper, we have explored several recent research articles that investigate these concepts in different types of fuzzy spaces, including intuitionistic fuzzy topological spaces, quasi-metric spaces, generalized metric spaces, generalized fuzzy topological spaces, intuitionistic fuzzy soft metric spaces, fuzzy normed linear spaces, fuzzy quasi-metric spaces, fuzzy metric spaces, and b-metric spaces. The methodology and results of each study vary based on the type of fuzzy space under consideration, but all papers aim to provide a better understanding of the properties and behavior of fuzzy connectedness and fuzzy continuity. Common theme across these articles includes the use of various types of fuzzy functions, fuzzy sets, and the extension of classical concepts to fuzzy spaces. This review paper provides a comprehensive overview of the recent advances in the study of fuzzy connectedness and fuzzy continuity, highlighting similarities and differences among the various types of fuzzy spaces and suggesting directions for future research

On the Intuitionistic fuzzy topological (metric and normed) spaces

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G_{\delta }$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa. Finally, we define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear operators and so we prove that every finite dimensional intuitionistic fuzzy normed space is complete.Comment: 16 page

Bipolar intuitionistic fuzzy CK compact spaces

The objective of this article is to initiate the innovative views on bipolar intuitionistic fuzzy topological space, bipolar intuitionistic fuzzy C compact and its preimage, orbit and image followed by some of its special characterizations are studied. The main approaches of its CK, RC compact spaces are established and few significant properties are investigated.Publisher's Versio

Some Topological Properties of Intuitionistic Fuzzy Normed Spaces

In 1986, Atanassov introduced the concept of intuitionistic fuzzy set theory which is based on the extensions of definitions of fuzzy set theory given by Zadeh. This theory provides a variable model to elaborate uncertainty and vagueness involved in decision making problems. In this chapter, we concentrate our study on the ideal convergence of sequence spaces with respect to intuitionistic fuzzy norm and discussed their topological and algebraic properties

Regular Semiopen Sets on Intuitionistic Fuzzy Topological Spaces in Sostak’s Sense

We introduce the concepts of fuzzy (r; s)-regular semi (resp. (r; s)-α, (r; s)-pre, (r; s)-β open sets, their respective interior and closure operators on intuitionistic fuzzy topological spaces in ˆ Sostak’s sense and then we investigate some of their characteristic properties