Topological concepts on certain fuzzy topological spaces including intuitionistic fuzzy topological spaces

Abstract

In this thesis the topological concepts of fuzzy topological spaces and intuitionistic fuzzy topological spaces were investigated and have been associated with their duals in classical topological spaces. Fuzzy sets, fuzzy points, fuzzy functions and fuzzy relations were presented along with their properties. Many topological concepts and properties were proved to be true in non fuzzy setting. Intuitionistic Fuzzy sets, Intuitionistic fuzzy points, Intuitionistic fuzzy functions and Intuitionistic fuzzy relations were presented along with their properties. Many topological concepts and properties were proved to be true in fuzzy setting. Also different approaches of separation axioms were investigated using Q-neighborhood and fuzzy points and Intuitionistic fuzzy points, and we studied another types of separation axioms on fuzzy setting and Intuitionistic fuzzy setting. Finally, fuzzy compactness and Intuitionistic fuzzy compactness were introduced with a theorem proved the way they are related.