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International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets

IWIFSGN 2018: Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives pp 58–68Cite as

Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1081))

Abstract

In this paper the definition of a multidimensional trapezoidal horizontal intuitionistic fuzzy number (TrHIFN) and multidimensional decomposition method (TrHIFN arithmetic) for calculations on TrHIFNs are presented. Till now, for intuitionistic fuzzy numbers (IFN) only low-dimensional approaches have been considered. The proposed arithmetic is based on multidimensional rdm interval arithmetic (RDMIA) and its extension horizontal fuzzy arithmetic (HFA). A direct result obtained with TrHIFN arithmetic is described in multidimensional space as a granule of information about the solution. From the direct solution, IFN as an indicator (a span) of the direct solution can be calculated. Moreover, in the paper the examples with basic operations on TrHIFN and the solution of intuitionistic fuzzy linear system (IFLS) are considered.

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Author information

Authors and Affiliations

  1. Department of Mathematical Methods, Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland

    Marek Landowski

Authors
  1. Marek Landowski
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Correspondence to Marek Landowski .

Editor information

Editors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering, Sofia, Bulgaria

    Vassia Atanassova

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

    Janusz Kacprzyk

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

    Andrzej Kaluszko

  5. WIT- Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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

    Jan W. Owsinski

  7. Intelligent Systems Laboratory, Faculty of Technical Sciences, Bourgas, Bulgaria

    Sotir Sotirov

  8. Intelligent Systems Laboratory, Prof. Assen Zlatarov University, Burgas, Bulgaria

    Evdokia Sotirova

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

    Eulalia Szmidt

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

    Slawomir Zadrozny

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Landowski, M. (2021). Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers. In: Atanassov, K., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives. IWIFSGN 2018. Advances in Intelligent Systems and Computing, vol 1081. Springer, Cham. https://doi.org/10.1007/978-3-030-47024-1_7

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