Preference modelling, a matter of degree

Bernard De Baets, J. Fodor

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationInternational Series in Operations Research and Management Science
PublisherSpringer New York LLC
Pages123-156
Number of pages34
Volume142
DOIs
Publication statusPublished - 2010

Publication series

NameInternational Series in Operations Research and Management Science
Volume142
ISSN (Print)08848289

Fingerprint

Preference Modelling
Decomposition
Fuzzy Preference
Fuzzy Preference Relation
Transitivity
Express
Quasi-copula
Preference Relation
Fuzzy Relation
Copula
Framework
Preference modelling
Generator
Cycle
Decompose
Fuzzy preference
Indifference
Preference relation
Preference structure

Keywords

  • Fuzzy relation
  • Preference structure
  • Reciprocal relation Cycle-transitivity
  • Transitivity

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Strategy and Management
  • Applied Mathematics
  • Computer Science Applications
  • Software

Cite this

Baets, B. D., & Fodor, J. (2010). Preference modelling, a matter of degree. In International Series in Operations Research and Management Science (Vol. 142, pp. 123-156). (International Series in Operations Research and Management Science; Vol. 142). Springer New York LLC. https://doi.org/10.1007/978-1-4419-5904-1_5

Preference modelling, a matter of degree. / Baets, Bernard De; Fodor, J.

International Series in Operations Research and Management Science. Vol. 142 Springer New York LLC, 2010. p. 123-156 (International Series in Operations Research and Management Science; Vol. 142).

Research output: Chapter in Book/Report/Conference proceedingChapter

Baets, BD & Fodor, J 2010, Preference modelling, a matter of degree. in International Series in Operations Research and Management Science. vol. 142, International Series in Operations Research and Management Science, vol. 142, Springer New York LLC, pp. 123-156. https://doi.org/10.1007/978-1-4419-5904-1_5
Baets BD, Fodor J. Preference modelling, a matter of degree. In International Series in Operations Research and Management Science. Vol. 142. Springer New York LLC. 2010. p. 123-156. (International Series in Operations Research and Management Science). https://doi.org/10.1007/978-1-4419-5904-1_5
Baets, Bernard De ; Fodor, J. / Preference modelling, a matter of degree. International Series in Operations Research and Management Science. Vol. 142 Springer New York LLC, 2010. pp. 123-156 (International Series in Operations Research and Management Science).
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