@misc{Szmidt_Eulalia._Autor_Similarity_2003,
 author={Szmidt, Eulalia. Autor and Kacprzyk, Janusz (1947– ). Autor},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2003},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 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.},
 title={Similarity on intuitionistic fuzzy sets and the Jaccard coefficient},
 type={Text},
 keywords={Fuzzy sets, Jaccard coefficient},
}