Analysis of system reliability based on weakest t-norm arithmetic operations using Pythagorean fuzzy numbers

The present study incorporates the weakest t-norm (T-w) based approximate Pythagorean fuzzy arithmetic operations on different types of Pythagorean fuzzy numbers to investigate the fuzzy reliability of a weapon system. In many real-world problems, sometimes due to the absence of adequate failure data of system components, the assessment of the precise probability of failure of system components may not be an easy task. Therefore, the failure data of system components can be assumed in fuzzy form. This study extends the concept of an intuitionistic fuzzy set into a Pythagorean fuzzy set, utilizing a novel approach to address the system failure probability with quantitative failure data of system components using fault tree analysis. In complex systems, interval arithmetic operations on fuzzy numbers may lead to an increasing tendency of fuzziness. To decrease the fuzzy spread up to a desired degree of accuracy during the complicated calculations of complex systems under an imprecise environment, approximate Pythagorean fuzzy arithmetic operations are developed based on the weakest t-norm methodology. Further, the fuzzy reliability of series and parallel systems is constructed using the aforesaid approach. The proposed study has been applied to a fault in a weapon system as an illustration.