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

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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, uninorm, intuitionistic fuzzy set

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Chicago
Deschrijver, Glad. 2009. “Non-conjunctive and Non-disjunctive Uninorms in Atanassov’s Intuitionistic Fuzzy Set Theory.” In Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, ed. JP Carvalho, DU Kaymak, and JMC Sousa, 184–188. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT).
APA
Deschrijver, Glad. (2009). Non-conjunctive and non-disjunctive uninorms in Atanassov’s intuitionistic fuzzy set theory. In JP Carvalho, D. Kaymak, & J. Sousa (Eds.), Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference (pp. 184–188). Presented at the Joint 2009 International Fuzzy Systems Association world congress and European Society for Fuzzy Logic and Technology conference (IFSA/EUSFLAT 2009), Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT).
Vancouver
1.
Deschrijver G. Non-conjunctive and non-disjunctive uninorms in Atanassov’s intuitionistic fuzzy set theory. In: Carvalho J, Kaymak D, Sousa J, editors. Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT); 2009. p. 184–8.
MLA
Deschrijver, Glad. “Non-conjunctive and Non-disjunctive Uninorms in Atanassov’s Intuitionistic Fuzzy Set Theory.” Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference. Ed. JP Carvalho, DU Kaymak, & JMC Sousa. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT), 2009. 184–188. Print.
@inproceedings{1257283,
  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.},
  author       = {Deschrijver, Glad},
  booktitle    = {Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference},
  editor       = {Carvalho, JP and Kaymak, DU and Sousa, JMC},
  isbn         = {9789899507968},
  language     = {eng},
  location     = {Lisbon, Portugal},
  pages        = {184--188},
  publisher    = {European Society for Fuzzy Logic and Technology (EUSFLAT)},
  title        = {Non-conjunctive and non-disjunctive uninorms in Atanassov's intuitionistic fuzzy set theory},
  year         = {2009},
}

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