An improved method to estimate the similarity between LR-type fuzzy numbers

Abstract

This paper presents an improved method for estimating the similarity between LR-type fuzzy numbers. By considering different left and right shape functions, we can conveniently compute the similarity between trapezoidal fuzzy numbers, Gaussian fuzzy numbers and normal fuzzy numbers. An algorithm for computing the proposed similarity measure between LR-type fuzzy numbers and a numerical method for approximating it are provided. Some of its properties are also examined. The performance of the proposed method is compared with some existing similarity measures through using different sets of LR-type fuzzy numbers. It is shown that the similarity between LR-type fuzzy numbers with parameters from any real number belonged to the real number set R is considered in the proposed method. The given similarity measure is scale-invariant and takes into account the shape of LR-type fuzzy numbers, which can overcome the shortcomings of existing methods.