Consistent fuzzy sets and decision making applications

The concept of fuzzy set, which can successfully mathematically model uncertain and conflicting information, is a widely used concept in the solution of multi-criteria decision making problems due to this feature. The aim of this thesis is to introduce a new fuzzy set concept in order to better model the uncertain information in the environment and to propose new decision methods for the solution of multi-criteria decision making problems. The thesis is organized as follows: The first chapter is devoted to the historical process of fuzzy set theory, its importance and its relationship with multi-criteria decision making theory. In the second part, basic definitions and examples related to fuzzy set theory are given. The third and fourth chapters constitute the original part of the thesis. In the third chap- ter, the consistency fuzzy set theory, which is a new fuzzy set generalization, is established, the concepts of correlation coefficient and cosine similarity measure for consistency fuzzy sets are proposed, and a multi-period medical diagnosis problem is solved. In the fourth chapter, the concepts of cross entropy and sine entropy measure for con- sistency fuzzy sets are studied and a multi-criteria decision making problem is solved by integrating these two concepts into the VIKOR (VIseKriterijumska Optimizacija I Kom- promisno Resenje) method. In the last chapter, a general evaluation of the thesis is given.