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A new attitude coupled with fuzzy thinking for solving fuzzy equations

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Abstract

With the development on the theory of fuzzy numbers, one of the major areas that emerged for the application of these fuzzy numbers is the solution of equations whose parameters are fuzzy numbers. The classical methods, involving the extension principle and \(\alpha \)-cuts, are too restrictive for solving fuzzy equations because very often there is no solution or very strong conditions must be placed on the equations so that there will be a solution. These facts motivated us to solve fuzzy equations with a new attitude. According to the new fuzzy arithmetic operations based on TA (in the domain of the transmission average of support), we discuss a new attitude solving fuzzy equations: \(A+X=B\), \(AX=B\), \(AX+B=C\), \(AX^{2}=B\), \(AX^{2}+B=C\) and \(AX^{2}+BX+C=D.\) Through theoretical analysis, by illustrative examples and computational results, we show that the proposed approach is more general and straightforward.

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Acknowledgements

The authors really appreciate Prof. Didier Dubois for his useful comments to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    T. Allahviranloo

  2. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

    I. Perfilieva

  3. Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

    F. Abbasi

Authors
  1. T. Allahviranloo
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  2. I. Perfilieva
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  3. F. Abbasi
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Correspondence to T. Allahviranloo.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants performed by any of the authors.

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Communicated by V. Loia.

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Allahviranloo, T., Perfilieva, I. & Abbasi, F. A new attitude coupled with fuzzy thinking for solving fuzzy equations. Soft Comput 22, 3077–3095 (2018). https://doi.org/10.1007/s00500-017-2562-2

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  • DOI: https://doi.org/10.1007/s00500-017-2562-2

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