On and#947; Generalized Closed Sets in Intuitionistic Fuzzy Topological Spaces

Abstract

Chapter 1 is divided into five sections which deals with the study of preliminary definitions and results on various already existing closed sets, continuous mappings, closed mappings, homeomorphisms and connectedness in intuitionistic fuzzy topological spaces which are used to accomplish the work. newlineIn Chapter 2, the first section gives a short introduction to intuitionistic fuzzy and#947; closed sets. In the second section we have introduced and studied a new class of sets called intuitionistic fuzzy and#947; generalized closed sets in intuitionistic fuzzy topological spaces. This section deals with the interrelation of our newly introduced sets with other type of intuitionistic fuzzy closed sets such as intuitionistic fuzzy semi closed sets, intuitionistic fuzzy pre closed sets, intuitionistic fuzzy regular closed sets, intuitionistic fuzzy and#945; closed sets, intuitionistic fuzzy semi-pre closed sets. Also it is shown that the converses are not true in general and they are proved with necessary counter examples. In section three, intuitionistic fuzzy and#947; generalized open sets are introduced and their interrelations with other intuitionistic fuzzy open sets are established. Also some of their properties are studied. In section four, we have introduced some theoretical application of intuitionistic fuzzy and#947; generalized closed sets and we have proved some interesting propositions. newlineIn Chapter 3, a new type of intuitionistic fuzzy continuous mapping called intuitionistic fuzzy and#947; generalized continuous mapping has been introduced. This chapter is divided into six sections. In the first section, we give a short introduction to intuitionistic fuzzy continuous mappings and irresolute mappings. In the second section, we have introduced intuitionistic fuzzy and#947; generalized continuous mappings and analyzed the interrelations between intuitionistic fuzzy and#947; generalized continuous mapping with other existing continuous mappings.