A Study on Second Order Fuzzy Soft Structures

Abstract

The present study is focused on second order fuzzy soft structures. The content of the research newlinework is given in six chapters. newlineThe concepts studied are newline(i) Second Order Fuzzy Soft Topological Spaces newline(ii) Second Order Fuzzy Soft Continuity and Second Order Fuzzy Soft Product Topology newline(iii) Different Versions of Hausdorff Separation Axiom in Second Order Fuzzy Soft newlineTopological Spaces newline(iv) Second Order Fuzzy Soft Proximity Structures and Second Order Fuzzy Soft Uniform newlineStructures newline(v) Second Order Fuzzy Soft Gradation of Openness newlineIn the first chapter, preliminary definitions of first order fuzzy topological spaces, soft newlinetopological spaces, first order fuzzy soft topological spaces and second order fuzzy topological spaces newlineare presented. newlineChapter 2 deals with second order fuzzy soft topological spaces. Definitions of second order newlinefuzzy soft sets and second order fuzzy soft topological spaces are introduced and their properties are newlinestudied in the first section. Connections between first order fuzzy soft, second order fuzzy soft, first newlineorder fuzzy and second order fuzzy topological spaces are analysed in the second section. Connections newlinebetween crisp topological spaces and second order fuzzy soft topological spaces are discussed in the newlinethird section. newlineIn chapter 3, second order fuzzy soft continuity and second order fuzzy soft product topology newlineare introduced. The definitions and properties are presented in the first two sections. In the third newlinesection, increasing second order fuzzy soft topology and continuous second order fuzzy soft topology newlineare introduced and analysed. newlineChapter 4 is devoted to the study of different versions of Hausdorff separation axiom in first newlineorder and second order fuzzy soft topological spaces. Hausdorff axioms in first order fuzzy newlinetopological spaces introduced by Gantner et al. (1978) and Katsaras (1981) are extended to first newlineorder fuzzy soft topological spaces in the first section and to second order fuzzy soft topological newlinespaces in the second section.