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

This paper demonstrates the practical application of interval-valued Pythagorean
triangular 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-v
PyTrFN. The paper also delves into the concept of cuts for i-v PyTrFNs, providing a detailed
analysis of their properties and applications in reliability analysis. This includes a discussion
of how cuts can be used to obtain crisp intervals from fuzzy sets, which can be useful for
reliability analysis. This paper presents a novel framework for reliability analysis using
interval-valued Pythagorean fuzzy sets. We define key reliability characteristics, such as
reliability, hazard rate, and mean time to failure, in the context of interval-valued Pythagorean
fuzzy uncertainty. The Pareto distribution is examined as a specific case, and the reliability of
series, parallel, and k-out-of-n systems is evaluated under this framework. This paper
contributes to the field of reliability engineering by providing interval-valued Pythagorean
fuzzy reliability (i-v PyTrFR) characteristics for specific cases of fuzzy scale parameters and
cut sets. A numerical example validates the proposed approach. Moreover, the reliability
analysis of series, parallel, and k-out-of-n systems highlights the potential of this framework
for addressing complex reliability problems.