Decomposition theorems and extension principles for hesitant fuzzy sets

Alcantud, Jose Carlos R.BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, Spain (author)

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We prove a decomposition theorem for hesitant fuzzy sets, which states that every typical hesitant fuzzy set on a set can be represented by a well-structured family of fuzzy sets on that set. This decomposition is expressed by the novel concept of hesitant fuzzy set associated with a family of hesitant fuzzy sets, in terms of newly defined families of their cuts. Our result supposes the first representation theorem of hesitant fuzzy sets in the literature. Other related representation results are proven. We also define two novel extension principles that extend crisp functions to functions that map hesitant fuzzy sets into hesitant fuzzy sets.

Torra, VicençHögskolan i Skövde,Institutionen för informationsteknologi,Forskningscentrum för Informationsteknologi,Skövde Artificial Intelligence Lab (SAIL)(Swepub:his)torv (author)
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, SpainInstitutionen för informationsteknologi (creator_code:org_t)

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NATURAL SCIENCES: NATURAL SCIENCES; and Computer and Inf ...; and Computer Science ...

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