Measuring Similarity and Ordering Based on Interval Type-2 Fuzzy Numbers

This paper extends a preference degree to rank interval type-2 fuzzy numbers. A general method to measure the similarity between interval type-2 fuzzy numbers is also introduced. Using some theorems and lemmas, it is proven that the extended similarity measures satisfy many common and desired properties based on the common axiomatic definitions introduced for similarity measures. The main properties of the extended preference degree are studied. In addition, several possible applications of the proposed methods are illustrated by some application examples in pattern recognition and multicriteria group decision making. Moreover, the proposed methods are examined in order to compare them with other existing methods, and the feasibility and effectiveness of the proposed methods are cleared via some lemmas and numerical comparisons.