2023-12-03T17:02:05Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/500982023-08-10T17:15:53Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Montero, Javier
author
Gómez, D.
author
Bustince, H.
2023-06-20T09:38:37Z
2023-06-20T09:38:37Z
2007
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0165-0114
10.1016/j.fss.2007.04.021
https://hdl.handle.net/20.500.14352/50098
http://www.sciencedirect.com/science/article/pii/S0165011407002126
http://www.sciencedirect.com
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.
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On the relevance of some families of fuzzy Sets.
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