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Issue:Non-conjunctive and non-disjunctive uninorms in Atanassov's intuitionistic fuzzy set theory

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Title of paper: Non-conjunctive and non-disjunctive uninorms in Atanassov's intuitionistic fuzzy set theory
Author(s):
Glad Deschrijver
Fuzziness and Uncertainty Modelling Research Unit, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B–9000 Gent, Belgium
Glad.Deschrijver@UGent.be
Presented at: Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009
Published in: Conference proceedings, pages 184—188
Download:  PDF (118  Kb, File info)
Abstract: Uninorms are a generalization of t-norms and t-conorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In real life applications, this kind of aggregation may be counter-intuitive. Atanassov's intuitionistic fuzzy set theory is an extension of fuzzy set theory which allows to model uncertainty about the membership degrees. In Atanassov's intuitionistic fuzzy set theory there exist uninorms which are neither conjunctive nor disjunctive. In this paper we study such uninorms more deeply and we investigate the structure of these uninorms. We also give several examples of uninorms which are neither conjunctive nor disjunctive.
Keywords: Conjunctive, disjunctive, interval-valued fuzzy set, intuitionistic fuzzy set, uninorm.
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