Similarity on intuitionistic fuzzy sets and the Jaccard coefficient

Szmidt, Eulalia; Kacprzyk, Janusz (1947– )

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Title: Similarity on intuitionistic fuzzy sets and the Jaccard coefficient

Abstract:

In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the counterparts of distances in the sense that dissimilarity is proportional to a distance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (under the assumption that dissimilarity behaves like a distance function between the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we compare and an element/object F we compare with, and a distance function between an element/object X we compare and a complement Fc of an element/object we compare with. We also examine a special case of the proposed similarity measure (entropy in the sense of De Luca and Termini axioms) and show that this special case is a counterpart of the Jaccard coefficient.In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the counterparts of distances in the sense that dissimilarity is proportional to a distance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (under the assumption that dissimilarity behaves like a distance function between the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we compare and an element/object F we compare with, and a distance function between an element/object X we compare and a complement Fc of an element/object we compare with. We also examine a special case of the proposed similarity measure (entropy in the sense of De Luca and Termini axioms) and show that this special case is a counterpart of the Jaccard coefficient.In this article we propose a new measure of similarity for intuitionistic fuzzy sets. The most commonly used similarity measures are just the counterparts of distances in the sense that dissimilarity is proportional to a distance between objects (elements, ...). The measure we propose ’’weights” both similarity and dissimilarity (under the assumption that dissimilarity behaves like a distance function between the objects). In other words, we take into account two kinds of a distance function: a distance function between an element/object X we compare and an element/object F we compare with, and a distance function between an element/object X we compare and a complement Fc of an element/object we compare with. We also examine a special case of the proposed similarity measure (entropy in the sense of De Luca and Termini axioms) and show that this special case is a counterpart of the Jaccard coefficient.