Geileralizations of Soft Expert Sets and Their Applications in Decision Analysis

Abstract

Researchers and mathematicians all over the world developed important analytical skills and problem-solving strategies to assess a broad range of issues in commerce, science and arts. But the most challenging issues were related to the problems which were more qualitative rather than quantitative in nature. Thus, the need to handle uncertain situations and vagueness in practical as well as theoretical problems led the researchers to the development of theories like fuzzy set theory. Many studies show that this theory may represent an important theoretical and practical tool to tackle uncertainty. In 1965, Zadeh initiated fuzzy sets. Fuzzy sets deal with possibilistic uncertainty connected with imprecision of states, perceptions and preferences. Zadeh extended the concept of fuzzy sets by interval valued fuzzy sets in 1975. Concept of intuitionistic fuzzy sets was introduced by Atanassov in 1983. To develop a model that is enriched with parameters, soft set theory was initiated by Molodtsov in 1999. It attracted the attention of many researchers as the theory proved its worth in many dimensions like medicine and decision analysis. Maji et al. discussed decision making problems through soft sets and fuzzy soft sets. Maji et al. defined the operations of union and intersection on soft sets. To analyze decision making problems, hesitant fuzzy set theory also proves pretty worthwhile. It was presented by Torra and Narukawa as a generalization of fuzzy set theory. Jun et al. introduced a new notion of cubic sets in 2011 by using a fuzzy sets and an interval-valued fuzzy sets. In 2011, Alkhazaleh et al. defined the concept of soft expert sets where the user can know the opinion of all the experts in one model. In this thesis, we introduce a generalization of soft expert sets defined by Alkhazaleh et al. which may be called graded soft expert (GSE) sets. We give three generalizations of soft expert sets named as graded soft expert sets, cubic soft expert sets and interval-valued intuitionistic fuzzy soft expert sets. Joint application of soft expert sets and other theories may result in a fruitful way in multi-criteria decision making. We also propose matrix algebra by using these generalizations. In each generalization, we propose an algorithm in decision analysis.