Reliability Evaluation of Phasor Measurement Unit Using Type-2 Fuzzy Set Theory

Practical applications inherently exhibit high levels of linguistic and numerical uncertainty. Conventional type-1 fuzzy sets have been employed in many real-world applications, but type-1 fuzzy sets use precise and crisp membership functions, which are unable to accommodate high levels of uncertainty. For example, the failure rate and the repair rate for any component of a system are uncertain; therefore, a membership representation using precise and crisp functions seems unreasonable from a pragmatic perspective. Type-2 fuzzy set theory represents a paradigm shift in which uncertainties related to the membership representation are incorporated through secondary membership functions. Whereas attempts have been made by researchers to accommodate the additional uncertainties related to linguistic and numerical data using type-1 fuzzy set theory, this paper investigates type-2 fuzzy set theory to address these uncertainties in an efficient way. The results of this study demonstrate the superiority of the proposed approach for analyzing the reliability of phasor measurement units, which are a technology so recent that the lack of sufficient field data creates a milieu of uncertainty.