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T-Ferrers Relations versus T-biorders

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2715))

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Abstract

In this paper, we study the Ferrers property of relations in the context of fuzzy preference modelling. A logical approach leads us to the notion of T-Ferrers relations, while a relational approach brings us to T-biorders. We characterize the t-norms for which both notions coincide. We also describe the kind of completeness exhibited by reflexive T-Ferrers relations or reflexive T-biorders. Finally, we investigate the relationship between the T-Ferrers properties of a reflexive fuzzy relation R and the corresponding strict preference relation P, and the relationship between R and P being T-biorders.

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Author information

Authors and Affiliations

  1. Department of Statistics and O.R., Faculty of Geology, University of Oviedo, Calvo Sotelo s/n, 33071, Oviedo, Spain

    Susana Díaz

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

    Bernard De Baets

  3. Department of Statistics and O.R., University of Oviedo, Nautical School, 33271, Gijón, Spain

    Susana Montes

Authors
  1. Susana Díaz
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  2. Bernard De Baets
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  3. Susana Montes
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Taner Bilgiç

  2. Dept. of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Okyay Kaynak

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© 2003 Springer-Verlag Berlin Heidelberg

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Díaz, S., De Baets, B., Montes, S. (2003). T-Ferrers Relations versus T-biorders. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_32

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  • DOI: https://doi.org/10.1007/3-540-44967-1_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40383-8

  • Online ISBN: 978-3-540-44967-6

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