Soft Computing

, Volume 22, Issue 9, pp 3077–3095 | Cite as

A new attitude coupled with fuzzy thinking for solving fuzzy equations

Methodologies and Application

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.

Keywords

Fuzzy arithmetics Fuzzy par Ambiguity rank Fuzzy equation Extension principle (EP) Transmission average (TA) 

Notes

Acknowledgements

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

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstravaCzech Republic
  3. 3.Department of Mathematics, Ayatollah Amoli BranchIslamic Azad UniversityAmolIran

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