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Development of Fuzzy Type-2 Reliability Models for Power System Reliability Evaluation Problems and Preventive Maintenance Suggestions

Sharma Anurag, Jha Manoj, Qureshi M.F.

System reliability modeling in terms of fuzzy set theory is basically utilizing the type-1 fuzzy sets, where the fuzzy membership is assumed as point-wise positive function ranging on [0,1]. Such a practice might not be practical because an interval valued membership may reflect the vagueness of system better according to human thinking patterns. The type-2 fuzzy set is more capable to handle the uncertainty of system using type-1 fuzzy set. The concept of type-2 fuzzy set (T2FS) was introduced by Zadeh (1965) as an extension of type-1 fuzzy set (ordinary fuzzy sets) to identify the uncertainties present in fuzzy systems. With fuzzy sets of higher type (e.g. type-2), the fuzziness of the relations is increased to handle inexact information. The interval type-2 fuzzy sets characterized with lower and upper membership function is recommended to use in reliability evaluation problems as it is easy for handling calculations in fuzzy planes. In this work, we explore the basics of the interval type-2 fuzzy sets theory and illustrate its application in terms of development of reliability models for Power system reliability evaluation problems and Preventive Maintenance (PM) suggestions with example.