A class of fuzzy multisets with a fixed number of memberships

  • Authors:

  • Benjamín Bedregal;Gleb Beliakov;Humberto Bustince;Tomasa Calvo;Radko Mesiar;Daniel Paternain

  • Affiliations:

  • Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil;School of Information Technology, Deakin University, Burwood, Australia;Department of Automatic and Computation, Public University of Navarra, Pamplona, Spain;Department of Automatic and Computation, University of Alcalá, Madrid, Spain;Slovak University of Technology, Bratislava, Slovakia;Department of Automatic and Computation, Public University of Navarra, Pamplona, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

The main aim of this work is to present a generalization of Atanassov's operators to higher dimensions. To do so, we use the concept of fuzzy set, which can be seen as a special kind of fuzzy multiset, to define a generalization of Atanassov's operators for n-dimensional fuzzy values (called n-dimensional intervals). We prove that our generalized Atanassov's operators also generalize OWA operators of any dimension by allowing negative weights. We apply our results to a decision making problem. We also extend the notions of aggregating functions, in particular t-norms, fuzzy negations and automorphism and related notions for n-dimensional framework.