Fuzzy mathematical structures and its applications

Abstract

The thesis deals mainly with fuzzy topological spaces, intuitionistic fuzzy sets, intuitionistic fuzzy topological spaces, fuzzy numbers, intuitionistic fuzzy numbers, interval-valued intuitionistic fuzzy numbers and applications of fuzzy mathematics. In chapter 1, the preliminaries of fuzzy topological space, intuitionistic fuzzy topological space, fuzzy numbers and interval-valued intuitionistic fuzzy sets are discussed. In chapter 2, a new notion of nearly intuitionistic fuzzy Hausdorff space is introduced. The relation between the existing notions of intuitionistic fuzzy Hausdorff space and the new notion of nearly intuitionistic fuzzy Hausdorff space are studied. The properties of nearly intuitionistic fuzzy Hausdorff space are studied. In chapter 3, a new notion of nearly intuitionistic fuzzy regular space is introduced and the relation with the existing notions of intuitionistic fuzzy regular space is studied. The properties of nearly intuitionistic fuzzy regular space are studied. In chapter 4, the notion of semi intuitionistic fuzzy Hausdorff spaces is introduced. Some of the theorems in semi-topological spaces in the crisp set up have been extended to new notion of semi intuitionistic fuzzy Hausdorff space in the intuitionistic fuzzy set up. In chapter 5, a new method of scoring to fuzzy numbers has been introduced and studied. The ranking of fuzzy numbers by Chen and Hwang s scores, centroid scores and proposed new scores are compared for some trapezoidal fuzzy numbers and triangular fuzzy numbers. In chapter 6, a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and studied. The proposed method is illustrated by numerical example and compared with other existing methods. In chapter 7, a new approach for multi-criteria group decision making problem under interval-valued intuitionistic fuzzy environment is established in which criterion values for alternatives are linguistic terms. newline