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An extension of fuzzy measures to multisets and its relation to distorted probabilities
Institut d'Investigacío en Intellig̀encia Artificial, Consejo Superior de Investigaciones Cient́ficas, Universitat Aut̀onoma de Barcelona, Bellaterra, Catalonia, Spain.ORCID iD: 0000-0002-0368-8037
Departments of Computer Science and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain / UNESCO Chair in Data Privacy, Tarragona, Catalonia, Spain.ORCID iD: 0000-0002-5040-2089
Toho Gakuen, Tokyo, Japan / Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan.
2012 (English)In: IEEE transactions on fuzzy systems, ISSN 1063-6706, E-ISSN 1941-0034, Vol. 20, no 6, 1032-1045 p.Article in journal (Refereed) Published
Abstract [en]

Fuzzy measures are monotonic set functions on a reference set; they generalize probabilities replacing the additivity condition by monotonicity. The typical application of these measures is with fuzzy integrals. Fuzzy integrals integrate a function with respect to a fuzzy measure, and they can be used to aggregate information from a set of sources (opinions from experts or criteria in a multicriteria decision-making problem). In this context, background knowledge on the sources is represented by means of the fuzzy measures. For example, interactions between criteria are represented by means of nonadditive measures. In this paper, we introduce fuzzy measures on multisets. We propose a general definition, and we then introduce a family of fuzzy measures for multisets which we show to be equivalent to distorted probabilities when the multisets are restricted to proper sets

Place, publisher, year, edition, pages
IEEE , 2012. Vol. 20, no 6, 1032-1045 p.
Keyword [en]
prime, fuzzy measure, distorted probability, multiset
National Category
Other Mathematics
URN: urn:nbn:se:his:diva-10682DOI: 10.1109/TFUZZ.2012.2191413ISI: 000311853200004ScopusID: 2-s2.0-84870502598OAI: oai:DiVA.org:his-10682DiVA: diva2:787981
Available from: 2013-04-25 Created: 2015-02-12 Last updated: 2015-08-05Bibliographically approved

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