Preference Modelling, a Matter of Degree

  • Bernard De Baets
  • János Fodor
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 142)


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.


Fuzzy relation Preference structure Transitivity Reciprocal relation Cycle-transitivity 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Biometrics and Process ControlGhent UniversityGentBelgium
  2. 2.Institute of Intelligent Engineering SystemsObuda UniversityBudapestHungary

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