ARROW-TYPE RESULTS UNDER INTUITIONISTIC FUZZY PREFERENCES

Gilbert Njanpong Nana and Louis Aime Fono ()
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Gilbert Njanpong Nana: Laboratoire de Mathématiques Appliquées, Ecole Nationale Supèrieure Polytechnique, B.P. 8390 Yaoundé, Cameroun
Louis Aime Fono: Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroun

New Mathematics and Natural Computation (NMNC), 2013, vol. 09, issue 01, 97-123

Abstract: Fonoet al.11characterized, for an intuitionistic fuzzyt-norm$\mathcal{T} = (T, S)$, two properties of a given regular intuitionistic fuzzy strict component of a(T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where$\mathcal{T} = (\min,\max)$. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.

Keywords: Intuitionistic fuzzy preference; regular intuitionistic fuzzy strict preference; (T; S)-transitivity; Arrow impossibility theorem; Gibbard oligarchy theorem (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S1793005713500075

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