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Preference Modelling, a Matter of Degree

In: Trends in Multiple Criteria Decision Analysis

Author

Listed:
  • Bernard Baets

    (Ghent University)

  • János Fodor

    (Obuda University)

Abstract

We consider various frameworks in which preferences can be expressed in a gradual way. The first framework is that of fuzzy preference structures as a generalization of Boolean (two-valued) preference structures. A fuzzy preference structure is a triplet of fuzzy relations expressing strict preference, indifference and incomparability in terms of truth degrees. An important issue is the decomposition of a fuzzy preference relation into such a structure. The main tool for doing so is an indifference generator. The second framework is that of reciprocal relations as a generalization of the three-valued representation of complete Boolean preference relations. Reciprocal relations, also known as probabilistic relations, leave no room for incomparability, express indifference in a Boolean way and express strict preference in terms of intensities. We describe properties of fuzzy preference relations in both frameworks, focusing on transitivity-related properties. For reciprocal relations, we explain the cycle-transitivity framework. As the whole exposition makes extensive use of (logical) connectives, such as conjunctors, quasi-copulas and copulas, we provide an appropriate introduction on the topic.

Suggested Citation

  • Bernard Baets & János Fodor, 2010. "Preference Modelling, a Matter of Degree," International Series in Operations Research & Management Science, in: Matthias Ehrgott & José Rui Figueira & Salvatore Greco (ed.), Trends in Multiple Criteria Decision Analysis, chapter 0, pages 123-156, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-5904-1_5
    DOI: 10.1007/978-1-4419-5904-1_5
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