SET THEORY’S EXTENSIONS-BASED ANALYSIS

Abstract

Firstly, as an attempt to overcome the difficulties of uncertainty, Black introduced the concept of vagueness. Then, Zadeh proposed an extension of the set theory which is the theory of fuzzy sets to deal with uncertainty. After that, Gau and Buehrer developed a new extension of the set theory called vague set theory, depending on Black’s definition of vagueness, to overcome the difficulties caused by the fuzzy set theory. Recently, Molodtsov suggested that one of the reasons for the difficulties using the fuzzy set theory and the vague set theory may be the parametrization tools inadequacy of those theories, so he introduced a completely new extension of the set theory for modeling uncertainty which is soft set theory. After introducing the soft set theory to deal with uncertainty associated with many real-life problems, a lot of sciences based on soft set theory have appeared and its applications have been used to solve complicated problems in economics, engineering and environment... etc. One of those sciences is the analysis studied in the sense of soft set theory.

The aim of this thesis is to study the concepts and theorems of the analysis associated with one of the recent extensions of soft set theory, which is the FS set theory. Furthermore, related matrices of other one of the recent extensions of soft set theory, which is the VS set theory, with the types, properties and operations of the VS matrices are introduced. Finally, applied real-life decision-making problems in medicine and education using the techniques of decision-making based on VS matrices are discussed.