Universidad Complutense de Madrid
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On the relevance of some families of fuzzy Sets.



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Montero, Javier y Gómez, D. y Bustince, H. (2007) On the relevance of some families of fuzzy Sets. Fuzzy Sets and Systems, 158 (22). pp. 2429-2442. ISSN 0165-0114

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0165011407002126

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In this paper we stress the relevance of a particular family of fuzzy sets, where each element can be viewed as the result of a classification problem. In particular, we assume that fuzzy sets are defined from a well-defined universe of objects into a valuation space where a particular graph is being defined, in such a way that each element of the considered universe has a degree of membership with respect to each state in the valuation space. The associated graph defines the structure of such a valuation space, where an ignorance state represents the beginning of a necessary learning procedure. Hence, every single state needs a positive definition, and possible queries are limited by such an associated graph. We then allocate this family of fuzzy sets with respect to other relevant families of fuzzy sets, and in particular with respect to Atanassov's intuitionistic fuzzy sets. We postulate that introducing this graph allows a natural explanation of the different visions underlying Atanassov's model and interval valued fuzzy sets, despite both models have been proven equivalent when such a structure in the valuation space is not assumed.

Tipo de documento:Artículo
Palabras clave:Atanassov’s intuitionistic fuzzy sets; Interval valued fuzzy sets; Type-2 fuzzy sets; L-fuzzy sets
Materias:Ciencias > Matemáticas > Lógica simbólica y matemática
Código ID:16327
Depositado:12 Sep 2012 11:08
Última Modificación:20 Abr 2016 16:48

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