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Characterizable fuzzy preference structures

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  • Bartel Van de Walle
  • Bernard De Baets
  • Etienne Kerre

Abstract

In this paper, we study the existence, construction and reconstruction of fuzzy preferencestructures. Starting from the definition of a classical preference structure, we propose anatural definition of a fuzzy preference structure, merely requiring the fuzzification of theset operations involved. Upon evaluating the existence of these structures, we discover thatthe idea of fuzzy preferences is best captured when fuzzy preference structures are definedusing a L Ú ukasiewicz triplet. We then proceed to investigate the role of the completenesscondition in these structures. This rather extensive investigation leads to the proposal of astrongest completeness condition, and results in the definition of a one-parameter class offuzzy preference structures. Invoking earlier results by Fodor and Roubens, the constructionof these structures from a reflexive binary fuzzy relation is then easily obtained. Thereconstruction of such a structure from its fuzzy large preference relation inevitable toobtain a full characterization of these structures in analogy to the classical case is morecumbersome. The main result of this paper is the discovery of a non-trivial characterizingcondition that enables us to fully characterize the members of a two-parameter class offuzzy preference structures in terms of their fuzzy large preference relation. As a remarkableside-result, we discover three limit classes of characterizable fuzzy preference structures,traces of which are found throughout the preference modelling literature. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Bartel Van de Walle & Bernard De Baets & Etienne Kerre, 1998. "Characterizable fuzzy preference structures," Annals of Operations Research, Springer, vol. 80(0), pages 105-136, January.
    • Handle: RePEc:spr:annopr:v:80:y:1998:i:0:p:105-136:10.1023/a:1018903628661
    DOI: 10.1023/A:1018903628661
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    Citations

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    Cited by:

    1. Bernard Baets & János Fodor, 1997. "Twenty years of fuzzy preference structures (1978–1997)," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 20(1), pages 45-66, June.
    2. repec:wut:journl:v:3:y:2012:id:1049 is not listed on IDEAS
    3. S. Chaudhari & S. Desai, 2014. "Transitive and acyclic rationality indicators of fuzzy choice functions on base domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 341-365, February.
    4. Haven, Emmanuel, 2002. "Fuzzy interval and semi-orders," European Journal of Operational Research, Elsevier, vol. 139(2), pages 302-316, June.
    5. Michaël Rademaker & Bernard De Baets, 2012. "Consistent union and prioritized consistent union: new operations for preference aggregation," Annals of Operations Research, Springer, vol. 195(1), pages 237-259, May.
    6. Hanna Borzęcka, 2012. "Multi-criteria decision making using fuzzy preference relations," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(3), pages 5-21.
    7. Susana Díaz & Bernard Baets & Susana Montes, 2011. "On the Ferrers property of valued interval orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 421-447, December.
    8. Doignon, Jean-Paul & Mitas, Jutta, 2000. "Dimension of valued relations," European Journal of Operational Research, Elsevier, vol. 125(3), pages 571-587, September.
    9. Van de Walle, Bartel & Turoff, Murray, 2009. "Fuzzy relations for the analysis of traders' preferences in an information market game," European Journal of Operational Research, Elsevier, vol. 195(3), pages 905-913, June.
    10. Georgescu, Irina, 2007. "Consistency indicators for fuzzy choice functions," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 93-105, January.

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