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Υ-values: power indices à la orness for non-additive measures
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0002-0368-8037
2024 (English)In: IEEE transactions on fuzzy systems, ISSN 1063-6706, E-ISSN 1941-0034, Vol. 32, no 7, p. 4099-4108Article in journal (Refereed) Published
Abstract [en]

Fuzzy measures, also known as capacities, nonadditive measures, and monotonic games, are increasingly usedin all kind of applications. Fuzzy measures are set functions. So, for a given set X, we need to define 2|X| − 2 parameters (excluding the measure on the empty set and on X itself). Becauseof that they are difficult to visualize, and indices and metrics havebeen defined. The Shapley value is an example. It permits us todetermine weights of importance of each element in X. In this paper we introduce an alternative index. We call it Υ-values. We provide an axiomatic characterization. These valuesare inspired on the Shapley values, and they are associated to setsize, or position (order statistics) in a chain. Thus, also positionwhen the measure is used in combination with a fuzzy integral. Andness and orness are measures that permit to evaluatethe degree of simultaneity (conjunction) and substitutability (disjunction) of an aggregation function. We show the connectionbetween our value and these concepts. In a way, Υ-values definea power index à la orness.

Place, publisher, year, edition, pages
IEEE, 2024. Vol. 32, no 7, p. 4099-4108
Keywords [en]
aggregation operators, andness, Distortion measurement, Fuzzy measures, Games, Indexes, Open wireless architecture, orness, Power measurement, Shapley values, Vectors, Weight measurement
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-224108DOI: 10.1109/TFUZZ.2024.3392268ISI: 001263598700009Scopus ID: 2-s2.0-85191317545OAI: oai:DiVA.org:umu-224108DiVA, id: diva2:1857945
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)The Kempe FoundationsAvailable from: 2024-05-15 Created: 2024-05-15 Last updated: 2025-04-24Bibliographically approved

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Torra, Vicenç

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