Similarity measures on trapezoidal fuzzy multi-numbers and their application to multiple criteria decision

In this thesis, concepts of fuzzy set, fuzzy numbers, multi-fuzzy set and similarity measures for TFMN's including Dice similarity measure, Jaccard similarity measure, Cosine similarity measure and Hybrid similarity measure which will be used in the next sections are given. Dice, Jaccard, Cosine and Hybrid similarity measures are defined to improve on the trapezoidal fuzzy multi-numbers and decision making methods for multi-criteria decision making problems have been studied with this similarity measures.Besides these; Weighted Dice, Weighted Jaccard, Weighted Cosine and Weighted Hybrid similarity measures are defined to develope the Trapezoidal Fuzzy Multi-Numbers.Also we investigate the propositions of the similarity measures. Additionally, multi-criteria decision making methods for TFMN are studied based on these given similarity measures. Practical examples are shown to approve the feasibility of the new methods. As a result, we compare the proposed methods with the existing methods in order to show the effectiveness and efficiency of the developed method in this thesis.