Raport Badawczy = Research Report ; RB/54/2003

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.

[8] pages ; 21 cm

Bibliografia s. [7,8]

Bibliography p. [7,8]

[8] stron ; 21 cm