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Preference Modelling, a Matter of Degree

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Trends in Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 142))

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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.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000, Gent, Belgium

    Bernard De Baets

  2. Institute of Intelligent Engineering Systems, Obuda University, Bécsi út 96/b, H-1034, Budapest, Hungary

    János Fodor

Authors
  1. Bernard De Baets
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  2. János Fodor
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Correspondence to Bernard De Baets .

Editor information

Editors and Affiliations

  1. Dept. Engineering Science, University of Auckland, Auckland, New Zealand

    Matthias Ehrgott

  2. Depto. Engenharia e Gestao, Instituto Superior Tecnico, Av. Prof.Dr. Cavaco Silva, Porto Salvo, 2780-990, Portugal

    José Rui Figueira

  3. Faculty of Economics, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Greco

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De Baets, B., Fodor, J. (2010). Preference Modelling, a Matter of Degree. In: Ehrgott, M., Figueira, J., Greco, S. (eds) Trends in Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 142. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5904-1_5

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