RT Journal Article
T1 On the relevance of some families of fuzzy Sets
A1 Gómez González, Daniel
A1 Montero De Juan, Francisco Javier
A1 Bustince, Humberto
AB 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.
PB Elsevier Science BV
SN 0165-0114
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50098
UL https://hdl.handle.net/20.500.14352/50098
LA eng
NO Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets and Systems. 158, 2429-2442 (2007). https://doi.org/10.1016/j.fss.2007.04.021
NO National Science Foundation (España)
DS Docta Complutense
RD 20 abr 2025