Carmen Torres-Blanc , Jesus Martinez-Mateo , Susana Cubillo , Luis Magdalena , Francisco Javier Talavera , Jorge Elorza
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引用次数: 0
Abstract
In this work we present a novel axiomatic framework for subsethood measures in type-2 fuzzy sets. It differs from previous approaches in two key ways. First, the degree of membership is not simply a fuzzy set as considered in other papers, but rather a label of the variable Truth, more in line with Zadeh's original idea. Secondly, the concept of subsethood is approached in terms of its relationship with cardinality. Additionally, illustrative examples of such measures are provided.
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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