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Decomposition theorems and extension principles for hesitant fuzzy sets
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, Spain.
University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. (Skövde Artificial Intelligence Lab (SAIL))ORCID iD: 0000-0002-0368-8037
2018 (English)In: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 41, p. 48-56Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 41, p. 48-56
Keywords [en]
Hesitant fuzzy set, Cut set, Decomposition theorem, Representation theorem, Extension principle
National Category
Computer Sciences
Research subject
Skövde Artificial Intelligence Lab (SAIL)
Identifiers
URN: urn:nbn:se:his:diva-14605DOI: 10.1016/j.inffus.2017.08.005ISI: 000417662100006Scopus ID: 2-s2.0-85027534671OAI: oai:DiVA.org:his-14605DiVA, id: diva2:1169548
Available from: 2017-12-28 Created: 2017-12-28 Last updated: 2018-02-01Bibliographically approved

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Torra, Vicenç

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  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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