Preference Modelling, a Matter of Degree

Bernard Baets () and János Fodor ()
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Bernard Baets: Ghent University
János Fodor: Obuda University

Chapter Chapter 5 in Trends in Multiple Criteria Decision Analysis, 2010, pp 123-156 from Springer

Abstract: 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.

Keywords: Fuzzy relation; Preference structure; Transitivity; Reciprocal relation; Cycle-transitivity (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4419-5904-1_5

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