Reliability of systems under different fuzzy environments
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Date
2015-07
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
The present work consists of five chapters. A brief summary of these chapters is given below.
The chapter one of the theses is purely introductory in nature and contains history related to reliability theory with several definitions of different reliability tools which are often used in the study of reliability theory. This chapter also discusses the fundamental concepts of fuzzy set theory and the need of fuzzy set theory in reliability evaluation. The chapter two contains review of literature which is a detailed survey of previous work done by different researchers and recent research papers related to reliability theory, fuzzy theory and fuzzy reliability theory. In the chapter three, different methods of reliability evaluation of the different systems using rough fuzzy set, intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, hesitant fuzzy set, trapezoidal fuzzy number and hexagonal fuzzy number have been developed. Some concepts about bifuzzy set and soft fuzzy set also introduced in this chapter. In the chapter four some numerical examples are presented to illustrate how to calculate the fuzzy reliability using different methods under different fuzzy environments. The results obtained from the examples illustrated in this research also support the traditional facts of the system reliability. Some new concepts about characterisations of α-cut in conflicting bifuzzy set theory and some new operations in soft intuitionistic fuzzy sets are also developed. In the final chapter, conclusions and future works are summarized. We can conclude from the present study that the proposed methods have no restrictions and it is applicable in situations where there are subjectivity, imprecision, uncertainty, ambiguity and hesitancy.
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