Fuzzy Reliability appraisal using interval-valued Pythagorean triangular Fuzzy number based on pareto lifetime distribution

This paper demonstrates the practical application of interval-valued Pythagoreantriangular fuzzy numbers (i-v PyTrFNs) in addressing uncertainty in reliability engineering.We focus on the Pareto lifetime distribution with a fuzzy scale parameter modeled by an i-vPyTrFN. The paper also delves into the concept of cuts for i-v PyTrFNs, providing a detailedanalysis of their properties and applications in reliability analysis. This includes a discussionof how cuts can be used to obtain crisp intervals from fuzzy sets, which can be useful forreliability analysis. This paper presents a novel framework for reliability analysis usinginterval-valued Pythagorean fuzzy sets. We define key reliability characteristics, such asreliability, hazard rate, and mean time to failure, in the context of interval-valued Pythagoreanfuzzy uncertainty. The Pareto distribution is examined as a specific case, and the reliability ofseries, parallel, and k-out-of-n systems is evaluated under this framework. This papercontributes to the field of reliability engineering by providing interval-valued Pythagoreanfuzzy reliability (i-v PyTrFR) characteristics for specific cases of fuzzy scale parameters andcut sets. A numerical example validates the proposed approach. Moreover, the reliabilityanalysis of series, parallel, and k-out-of-n systems highlights the potential of this frameworkfor addressing complex reliability problems.