on Beta double star Generalized Closed Sets in Intuitionistic Fuzzy Topological Spaces

Abstract

Topological structures on the collection of data are suitable mathematical models for mathematizing not only quantitative data but also qualitative ones. Closedness is the basic concept for the study and investigation in topological spaces. Topology is used in nearly all branches of mathematics in one form or another. It is the mathematical study of the properties that are preserved through deformations, twisting and stretching of objects. Topology is implemented recently to understand diverse topics, such as cell biology, superconductors, robot motion and etc. The first work on Topology came into existence due to Euler, when he published the solution to the Konigsberg bridge problem. newlineFuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. The notion of fuzzy set theory has caused great interest among both pure and applied mathematicians. Classical mathematical methods are not enough to solve the problems of daily life and also are not enough to meet the new requirements. Therefore, some theories such as fuzzy set theory have been developed to solve these problems. Applications of this theory appear in topology and many areas of mathematics. The first publication in fuzzy set theory by Zadeh (1965) and then by Goguen (1967) shows the intention of the authors to generalize the classical set. Through fuzzy sets we can speak only about membership values and it does not give a correct answer for non-membership values. newlineAtanassov (1986), a Bulgarian mathematician, created an idea about the non-membership value and then he introduced a new set which includes the non-membership value and coined the set as intuitionistic fuzzy set where the degree of membership is denoted by and#61549;A(x) and#61646; [0, 1] of each element x and#61646; X to a set A and the degree of non-membership is denoted by and#61550;A(x) and#61646; [0, 1] . newlineIntuitionistic fuzzy set is a generalized notion to include both fuzzy sets and vague sets. Intuitionistic fuzzy sets have been found in diverse applied areas of science and technology and have been appli