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Correct Solution of Fuzzy Linear System Based on Interval Theory

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 889))

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Abstract

In this paper authors would like to make a critical review of the low-dimensional method proposed in [3] by Allahviranloo and Gandavi for solving fuzzy linear system with crisp square matrix and a fuzzy right-hand side vector. The solution presented in the mentioned work is, in general incorrect. The authors prove that given method is incorrect and propose an alternative solution based on multidimensional Relative-Distance-Measure (RDM) interval arithmetic and fuzzy RDM interval arithmetic that gives correct results.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Żołnierska 49, 71-210, Szczecin, Poland

    Andrzej Piegat & Marcin Pietrzykowski

Authors
  1. Andrzej Piegat
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  2. Marcin Pietrzykowski
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Corresponding author

Correspondence to Marcin Pietrzykowski .

Editor information

Editors and Affiliations

  1. West Pomeranian University of Technology in Szczecin, Szczecin, Poland

    Jerzy Pejaś

  2. West Pomeranian University of Technology in Szczecin , Szczecin, Poland

    Imed El Fray

  3. West Pomeranian University of Technology in Szczecin, Szczecin, Poland

    Tomasz Hyla

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

    Janusz Kacprzyk

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Piegat, A., Pietrzykowski, M. (2019). Correct Solution of Fuzzy Linear System Based on Interval Theory. In: Pejaś, J., El Fray, I., Hyla, T., Kacprzyk, J. (eds) Advances in Soft and Hard Computing. ACS 2018. Advances in Intelligent Systems and Computing, vol 889. Springer, Cham. https://doi.org/10.1007/978-3-030-03314-9_6

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