Similarity functions for generalized trapezoidal fuzzy numbers: An improved comparative analysis

Abstract

Different functions for quantifying the degree of similarity between two fuzzy numbers have been proposed in the literature on the basis of various descriptive parameters, such as the geometric distance, the distance between the centers of gravity, the perimeters or the shared area between the fuzzy numbers. However, these similarity functions are not equally applicable across all situations. Consequently, comparative analyses have been performed on the basis of different sets of fuzzy number pairs. In this paper we thoroughly review the similarity functions proposed in the literature, identify their properties and possible drawbacks and compare them on the basis of an extended set of fuzzy numbers.

An improvised similarity measure for generalized fuzzy numbers

“…The data of 11 sets of fuzzy numbers in [23] are used to compare the similarity values of the proposed similarity measure with the existing similarity measures. These sets are commonly used by many [24][25][26] as a comparison and benchmarking tool. The similarity values obtained is as in Table 1.…”