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Intelligent Systems'2014 pp 341–352Cite as

Interval-Valued Fuzzy Preference Relations and Their Properties

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 322))

Abstract

In the paper properties of interval-valued fuzzy preference relations are considered and preservation of a preference property by some operations, including lattice operations, the converse and the complement relations are studied. The concept of a preference relation presented here is a generalization of the concept of crisp preference relations. Moreover, weak properties of interval-valued fuzzy relations, namely reflexivity, irreflexivity, connectedness, asymmetry, antisymmetry, transitivity, and moderate transitivity are defined. Furthermore, the assumptions under which interval-valued fuzzy preference relations fulfil the mentioned properties are proposed.

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Authors and Affiliations

  1. Department of Mathematics and Natural Sciences, University of Rzeszów, Al. Rejtana 16 C, 35-959, Rzeszów, Poland

    Urszula Bentkowska

Authors
  1. Urszula Bentkowska
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Correspondence to Urszula Bentkowska .

Editor information

Editors and Affiliations

  1. School of Computing and Communications, Lancaster University, Lancaster, United Kingdom

    P. Angelov

  2. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K.T. Atanassov

  3. Intelligent Systems Department, Bulgarian Academy of Sciences Inst. of Infor. & Communication Techn., Sofia, Bulgaria

    L. Doukovska

  4. Metalurgy, University of Chemical Technology and, Sofia, Bulgaria

    M. Hadjiski

  5. University of Library Studies and IT (ULSIT), Sofia, Bulgaria

    V. Jotsov

  6. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    J. Kacprzyk

  7. Knowledge Engineering and Discovery Research Institute, Auckland University of Technology, Auckland, New Zealand

    N. Kasabov

  8. Intelligent Systems Laboratory, Prof. Assen Zlatarov University Faculty of Technical Sciences, Bourgas, Bulgaria

    S. Sotirov

  9. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    E. Szmidt

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    S. Zadrożny

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© 2015 Springer International Publishing Switzerland

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Bentkowska, U. (2015). Interval-Valued Fuzzy Preference Relations and Their Properties. In: Angelov, P., et al. Intelligent Systems'2014. Advances in Intelligent Systems and Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-11313-5_31

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  • DOI: https://doi.org/10.1007/978-3-319-11313-5_31

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11312-8

  • Online ISBN: 978-3-319-11313-5

  • eBook Packages: EngineeringEngineering (R0)

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