General representation theorems for fuzzy weak orders

Ulrich Bodenhofer, Bernard De Baets, J. Fodor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The present paper gives a state-of-the-art overview of general representation results for fuzzy weak orders. We do not assume that the underlying domain of alternatives is finite. Instead, we concentrate on results that hold in the most general case that the underlying domain is possibly infinite. This paper presents three fundamental representation results: (i) score function-based representations, (ii) inclusion-based representations, (iii) representations by decomposition into crisp linear orders and fuzzy equivalence relations.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages229-244
Number of pages16
Volume4342 LNAI
DOIs
Publication statusPublished - 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4342 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Fingerprint

Weak Order
Representation Theorem
Decomposition
Fuzzy Equivalence Relation
Score Function
Linear Order
Inclusion
Decompose
Alternatives

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bodenhofer, U., De Baets, B., & Fodor, J. (2006). General representation theorems for fuzzy weak orders. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4342 LNAI, pp. 229-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4342 LNAI). https://doi.org/10.1007/11964810_11

General representation theorems for fuzzy weak orders. / Bodenhofer, Ulrich; De Baets, Bernard; Fodor, J.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4342 LNAI 2006. p. 229-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4342 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bodenhofer, U, De Baets, B & Fodor, J 2006, General representation theorems for fuzzy weak orders. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4342 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4342 LNAI, pp. 229-244. https://doi.org/10.1007/11964810_11
Bodenhofer U, De Baets B, Fodor J. General representation theorems for fuzzy weak orders. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4342 LNAI. 2006. p. 229-244. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11964810_11
Bodenhofer, Ulrich ; De Baets, Bernard ; Fodor, J. / General representation theorems for fuzzy weak orders. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4342 LNAI 2006. pp. 229-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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