Fuzzy continuity of functions in the fuzzy topological spaces

ABSTRACT This study, purpose to give fuzzy weakly continuity, fuzzy almost continuity, fuzzy quasi continuity, fuzzy somewhat continuity, fuzzy rarely continuity, fuzzy D-continuity and weakly forms of them with the relations, are four chapters. In the first chapter are given introductory information about fuzzy sets and fuzzy topological spaces. Also some definitions and theorems and their references, in this area are given. The second, the third and the forth chapters offer the original studies of this thesis. In the second chapter which takes from three sections, fuzzy waekly and fuzzy weakly* continuities are defined and compared with fuzzy weakly** continuity. Alsoit is shown some examples that they are independent to each other. In the second section, fuzzy almost cotinuity is defined in the sense of Stallings and studied the relations with the other fuzzy almost continuities. Also, some characterizations of the fuzzy almost continuity in the sense of Singal are given. In the last section, fuzzy quasi and fuzzy somewhat continuity are compared with weakly forms of them. In the third chapter, some basic properties of fuzzy rarely continuity of functions are studied. Then, fuzzy rarely* continuity is defined and compared with some continuities and their weakly forms. The strongly and weakly forms of fuzzy 0-continuity of functions are defined. Also fuzzy strongly 8* -continuity is defined. Then, some comparisons are done. In the last chapter takes from two sections. In the first section, fuzzy D-continuity and fuzzy D*-continuity of functions are defined and equivalent conditions are given. Then several properties and requirements are studied. In the second section, some properties which are preserved under the fuzzy D-continuity of functions are studied. This section is finished with the definitions of fuzzy D-Hausdorff space and fuzzy D-regular space and some properties of them.