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Twenty years of fuzzy preference structures (1978–1997)

Vent’anni di struttura di preferenza fuzzy

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Abstract

The aim of this paper is to summarize the historical development of the concept of a fuzzy preference structure and to present the resulting material in a logical manner. Roughly speaking, three phases can be distinguished. In the first phase, different proposais for constructing fuzzy strict preference and indifference relations emerge. In the second one, this construction is approached in an axiomatic way, by imposing couditions on the fuzzy strict preference, indifference and incomparability relations, leading to functional equations identifying suitabie strict preference, indifference and incomparability generators. Surprisingly, the detinition of a fuzzy preference structure was only given in the third phase, leading to the study of additive fuzzy preference structures. Combined with results from the axiomatic approach, this has linally led to the discovery of characterizable fuzzy preference structures.

Riassunto

Scopo di questo lavoro è quello di riassumere lo sviluppo storico del concetto di struttura di preferenza fuzzy e presentare i risultati in modo logico.

Si possono approssimativamente distinguere tre fasi. Nella prima emergono diverse proposte per costruite relazioni fuzzy di preferenza stretta ed indifferenza.

Nella seconda fase questa costruzione viene affrontata in modo assiomatico imponendo condizioni che conducono alle equazioni funzionali che identificano i generatori di preferenza stretta, indifferenza e non confrontabilità.

E sorpredente che la definizione di struttura di preferenza fuzzy sia stata solo la terza fase, che conduce allo studio delle preferenze fuzzy additive.

Combinata con i risultati derivanti dall»pproccio assiomatico, questa fase ha fiualmente condotto alla caratterizzazione della struttura di preferenza fuzzy.

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Authors and Affiliations

  1. Department of Applied Mathematics & Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000, Gent, Belgium

    Bernard de Baets

  2. Institute of Mathematics and Compuler Science, University of Agricultural Sciences (GATE), Gödöllö, Hungary

    János C. Fodor

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  1. Bernard de Baets
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  2. János C. Fodor
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Correspondence to Bernard de Baets.

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de Baets, B., Fodor, J.C. Twenty years of fuzzy preference structures (1978–1997). Decisions Econ Finan 20, 45–66 (1997). https://doi.org/10.1007/BF02688988

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