Antonio Francisco Roldán López de Hierro , Concepción Roldán , Carlos Guerra , Javier Fernández , Anderson Cruz , Ronei Marcos de Moraes , Humberto Bustince
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From type-(2,k) grouping indices to type-(2,k) Jaccard indices
In this work, we introduce the notion of grouping index for type-2 fuzzy sets as a measure of how far the union of two type-2 fuzzy sets over the same universe is from the total universe. We also show how we can extend the notion of the Jaccard index to the type-2 setting by means of type-2 grouping and overlap indexes.
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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