New Similarity Measures Between Generalized Trapezoidal Fuzzy Numbers Using the Jaccard Index

Abstract

Similarity measures between generalized trapezoidal fuzzy numbers (GTFNs) are employed to indicate the degrees of similarity between GTFNs. Although several similarity measures of GTFNs have been proposed in the literature, none has considered using the Jaccard index. In general, the Jaccard index is a statistic used for comparing the similarity and diversity of sample sets. This paper presents a new similarity measure between GTFNs, which involves the Jaccard index. The proposed similarity measure is found to have better properties. Several examples are employed to compare the proposed measure with some existing methods. An experiment is performed using 15 sets of GTFNs to compare the proposed similarity measure with existing ones. Numerical results show that the proposed measure is more reasonable than those existing methods.