System reliability analysis based on different types of Pythagorean fuzzy failure rates of components

Abstract

To examine the system reliability, fuzzy sets and intuitionistic fuzzy sets have been used in the past, however, this study extends the concept of an intuitionistic fuzzy set into a Pythagorean fuzzy set. More often failure rates of all components of a system do not follow the same types of fuzzy numbers. Hence, the current study is focused on evaluating the reliability of some systems in a fuzzy environment using different kinds of Pythagorean fuzzy numbers. To incorporate the aforementioned situations this paper introduces a method for analyzing the fuzzy reliability of systems wherein components follow different types of Pythagorean fuzzy numbers. In order to construct the membership and non-membership functions of fuzzy reliability, non-linear programming techniques are applied to compute functions of Pythagorean fuzzy numbers. In the proposed method, membership and non-membership functions of the series, parallel, parallel-series, and series-parallel systems are studied. Numerical illustrations are presented at the end to demonstrate the fuzzy reliability of the systems using the proposed environment.