Intuitionistic Fuzzy Semi γ* Generalized Closed Sets

Abstract

The Aim of this thesis is to introduce a new class of sets called semi and#947;* generalized closed sets in intuitionistic fuzzy topological space. Further, the corresponding open sets, theoretical applications, continuous mappings, almost continuous mappings, contra continuous mappings, almost contra continuous mappings, irresolute mappings, completely continuous mappings, perfectly continuous mapping, closed mappings, open mappings, almost closed mappings, contra open mappings, almost contra open mappings, connectedness and compactness are being defined. Their respective properties, theorems, interrelations between the various closed sets are discussed with necessary counter examples. newlineAlso we have obtained the dependency of intuitionistic fuzzy semi and#947;* generalized closed sets with other existing closed sets in intuitionistic fuzzy topological space. The complement of intuitionistic fuzzy semi and#947;* generalized closed sets are called intuitionistic fuzzy semi and#947;* generalized open sets. newlineVarious types of continuous mappings called intuitionistic fuzzy semi and#947;* generalized continuous mappings, intuitionistic fuzzy contra semi and#947;* generalized continuous mappings, intuitionistic fuzzy almost semi and#947;* generalized continuous mappings, intuitionistic fuzzy completely semi and#947;* generalized continuous mappings and intuitionistic fuzzy semi and#947;* generalized irresolute mappings are defined and their properties are analyzed. newlineThe notion of intuitionistic fuzzy semi and#947;* generalized closed mappings, intuitionistic fuzzy semi and#947;* generalized open mappings and intuitionistic fuzzy contra semi and#947;* generalized open mappings are introduced and their properties are discussed. newlineBy using the notion of intuitionistic fuzzy connectedness we have introduced intuitionistic fuzzy semi and#947;* generalized connected space and intuitionistic fuzzy semi and#947;* generalized super connected space. Their properties are investigated and intuitionistic fuzzy semi and#947;* generalized super connected space is characterized.