Uncertain multiplicative linguistic soft sets belief interval valued soft set in fuzzy expert system and their applications

Abstract

The paramount intention of this thesis is to extended the soft set theory to linguistic variables and belief theory. Based on linguistic variables we introduce the notions of uncertain multiplicative linguistic soft set and 2-Dimensional linguistic soft set. Using belief theory (Dempster-Shafer) we introduce the notion of belief interval-valued soft set and fuzzy-valued D number soft set. The first chapter discusses the literature survey of the soft newlineset and related definitions needed for the development of this thesis. Linguistic variable play an important role in evaluating the data and in approximate reasoning . It is gives more accuracy of the given data. Many theories have been developed to deal with uncertainty of various fields. Soft set is one of such theory that is used to solve the uncertainty situation in an effective manner. It is free from the parameters. Combining the soft sets and linguistic newlinevariables we introduce the uncertain multiplicative linguistic soft sets in Chapter 2. Some algebraic operations, decision making algorithm and student learning processes combined with expert system are also developed in this chapter. 2-Dimensional linguistic variable is a hybrid theory of linguistic variable. Evaluation of given data by using 2-Dimensional linguistic variable has two parts namely one is the linguistic evaluation and another one is the reliability of linguistic variable. Based on 2-Dimensional linguistic variable and soft set we introduce a hybrid structure called 2-Dimensional linguistic soft set in Chapter 3. Some algebraic operations, similarity and distance measures of 2-Dimensional linguistic soft sets are defined. Finally, a decision making algorithm and suitable example are also given in this chapter. newline newline