Ranking Fuzzy Numbers by Similarity Measure Index

Abstract

Uncertainties included in soft classification exist in classical mathematics. However, in daily life, the extended fuzzy concept has much information and due to the large applications of fuzzy numbers, the ranking of numbers plays a very important role in linguistic decision-making and some other fuzzy application systems. Moreover, several strategies have been proposed for ranking of fuzzy numbers. However, due to the complexity of the problem, a method gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcoming, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different rankings for the same situation and some method cannot rank crisp numbers. In 2011, Hajjari [1, 2] proposed an approach for similarity measure for a triangular fuzzy numbers (TFNs), which computed the distance between two fuzzy numbers and used centroid point namely Index. In previous method, the rejected centroid point is used. However, this method has two main weaknesses including rejected formula and similarity measure for only TFNs. For overcoming the above issues, a new similarity measure index to calculate the degree of similarity of generalized trapezoidal fuzzy numbers (TrFNs) is proposed. The proposed approach is developed by integrating the concept of center of gravity points and distance of fuzzy numbers. The proposed method gives a better and more robust similarity measure and it is more efficient than previous one and other methods in the literature as well. The method is illustrated by some numerical examples and in particular, the results of ranking by the given method and some common and existing methods for ranking is compared to confirm the advantages of presented approach.