Soft Computing

, Volume 23, Issue 10, pp 3383–3396 | Cite as

Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers

  • F. AbbasiEmail author
  • T. Allahviranloo
Methodologies and Application


This paper presents a new practical method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average (TA) (Abbasi et al. in J Intell Fuzzy Syst 29:851–861, 2015) on Rational-linear patchy fuzzy numbers. The concept of fuzzy numbers is extended by idea of Rational-linear patchy fuzzy numbers. Then, we have introduced fuzzy arithmetic operations of TA between two Rational-linear patchy fuzzy numbers. Finally, a new method has been developed for analyzing the fuzzy system reliability of series and parallel systems based on the fuzzy arithmetic operations of TA, where the reliability of each component is represented by a Rational-linear patchy fuzzy number. A technical example is given to illustrate applying the method and comparing the results of the new method with the previous methods. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.


TA operations Rational-linear patchy fuzzy number Fuzzy system reliability Statistical data 



The authors are grateful to anonymous referees whose valuable comments helped to improve the content of this paper.

Compliance with ethical standards

Conflicts 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 GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Ayatollah Amoli BranchIslamic Azad UniversityAmolIran
  2. 2.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran

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