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The Use of Belief Intervals in Operations on Intuitionistic Fuzzy Values

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Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

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Abstract

This paper presents a critical analysis of conventional operations on intuitionistic fuzzy values (IFVs) and their applicability to the solution of multiple criteria decision making (MCDM) problems in the intuitionistic fuzzy setting. A set of operations on IFVs based on the interpretation of intuitionistic fuzzy sets in the framework of the Dempster-Shafer theory of evidence (DST) is proposed and analyzed. This interpretation makes it possible to represent mathematical operations on IFVs as operations on belief intervals. The corresponding method for aggregation of local criteria presented by IFVs in the framework of DST is proposed and analyzed. The proposed approach allows us to solve MCDM problems without intermediate defuzzification when not only criteria, but their weights are IFVs. The advantages of the proposed approach are illustrated by numerical examples.

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Author information

Authors and Affiliations

  1. Institute of Comp. & Information Sci., Czestochowa University of Technology, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Ludmila Dymova, Pavel Sevastjanov & Kamil Tkacz

Authors
  1. Ludmila Dymova
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  2. Pavel Sevastjanov
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  3. Kamil Tkacz
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Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, Computer Science Division, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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© 2012 Springer-Verlag Berlin Heidelberg

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Dymova, L., Sevastjanov, P., Tkacz, K. (2012). The Use of Belief Intervals in Operations on Intuitionistic Fuzzy Values. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_27

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  • DOI: https://doi.org/10.1007/978-3-642-29347-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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