Arrow’s theorem and max-star transitivity

Duddy, Conal; Perote‐Peña, Juan; Piggins, Ashley

doi:10.1007/s00355-010-0461-x

Cited by 17 publications

(2 citation statements)

References 32 publications

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“…Furthermore, the fact of existence of different non-equivalent kinds of transitivity definitions and connectedness as well as completeness (see also [27][28][29][30]), tells us that the consideration in the fuzzy context of some kind of fuzzy total preorder is not unique. (Other non-equivalent definitions of transitivity have been introduced in this literature, see e.g., [27,28,31,32]). We should choose a suitable type.…”

Section: Remarkmentioning

confidence: 99%

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

2020

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We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

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Section: Remarkmentioning

confidence: 99%

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

2020

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“…Despite all this variety of models, we will focus on one of the most extended families of extensions (used e.g. in [3,10,15]). This family of models is characterized by a t-norm modelling the juxtaposition (intersection) and a t-conorm modelling the conjunction (union) in the fuzzy set framework.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Arrovian Theorems when preferences are complete

Raventós-Pujol¹

2021

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In this paper we study the aggregation of fuzzy preferences on nonnecessarily finite societies. We characterize in terms of possibility and impossibility a family of models of complete preferences in which the transitivity is defined for any t-norm. For that purpose, we have described each model by means of some crisp binary relations and we have applied the results obtained by Kirman and Sondermann.

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