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Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory

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Abstract
In this paper we propose an extension of the well-known OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov’s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction of the OWA function involves reordering the input values, we propose a way of transforming the input values in IVFS and AIFS theory to a new list of input values which are now ordered.
Keywords
quasi-arithmetic mean, arithmetic mean, Aggregation function, Atanassov’s intuitionistic fuzzy set, T-NORMS, CONORMS, AGGREGATION OPERATORS, interval-valued fuzzy set, TRUTH VALUES, COMPENSATORY OPERATORS, OWA function

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Chicago
Deschrijver, Glad. 2011. “Quasi-arithmetic Means and OWA Functions in Interval-valued and Atanassov’s Intuitionistic Fuzzy Set Theory.” In Advances in Intelligent Systems Research, ed. S Galichet, J Montero, and G Mauris, 506–513. Paris, France: Atlantis Press.
APA
Deschrijver, Glad. (2011). Quasi-arithmetic means and OWA functions in interval-valued and Atanassov’s intuitionistic fuzzy set theory. In S. Galichet, J. Montero, & G. Mauris (Eds.), Advances in Intelligent Systems Research (pp. 506–513). Presented at the 7th Biannual conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) ; 17th Annual LFA meeting, Paris, France: Atlantis Press.
Vancouver
1.
Deschrijver G. Quasi-arithmetic means and OWA functions in interval-valued and Atanassov’s intuitionistic fuzzy set theory. In: Galichet S, Montero J, Mauris G, editors. Advances in Intelligent Systems Research. Paris, France: Atlantis Press; 2011. p. 506–13.
MLA
Deschrijver, Glad. “Quasi-arithmetic Means and OWA Functions in Interval-valued and Atanassov’s Intuitionistic Fuzzy Set Theory.” Advances in Intelligent Systems Research. Ed. S Galichet, J Montero, & G Mauris. Paris, France: Atlantis Press, 2011. 506–513. Print.
@inproceedings{2128193,
  abstract     = {In this paper we propose an extension of the well-known OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov{\textquoteright}s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction of the OWA function involves reordering the input values, we propose a way of transforming the input values in IVFS and AIFS theory to a new list of input values which are now ordered.},
  author       = {Deschrijver, Glad},
  booktitle    = {Advances in Intelligent Systems Research},
  editor       = {Galichet, S and Montero, J and Mauris, G},
  isbn         = {9789078677000},
  issn         = {1951-6851},
  language     = {eng},
  location     = {Aix-les-Bains, France},
  pages        = {506--513},
  publisher    = {Atlantis Press},
  title        = {Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory},
  url          = {http://dx.doi.org/10.2991/eusflat.2011.144},
  year         = {2011},
}

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