FUZZY RELIABILITY STUDIES USING VAGUE SETS AND ITS APPLICATIONS

Abstract

The work being presented in the present thesis is devoted to the study of various methods to analyze the fuzzy system reliability using different extensions of vague sets. The chapter-wise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes mathematical definitions, operations and concepts used throughout the work. It also presents brief review of the work done in the area of fuzzy reliability analysis. In Chapter 2, the concept of trapezoidal fuzzy numbers [95] is extended to trapezoidal vague sets. Also, definition of trapezoidal vague set and arithmetic operations between two trapezoidal vague sets are introduced. Further a method is developed for analyzing the fuzzy reliability of series, parallel, series-parallel and parallel-series systems using trapezoidal vague sets, where the reliability of each component of a system is represented by a trapezoidal vague set defined on the universe of discourse [0, 1]. The developed method is applied to analyze the fuzzy reliability of a marine power plant. Chapter 3, consists of a new method for analyzing the fuzzy reliability of series, parallel, series-parallel and parallel-series networks having three state devices, where the reliability of each component of a system is represented by a trapezoidal vague set [54] defined on the universe of discourse [0, 1]. In Chapter 4, the concept of triangular vague sets [25, 26] is extended to interval valued triangular vague sets. Also arithmetic operations between them are defined. Using this concept, a method is developed for analyzing the fuzzy reliability of series, parallel, series-parallel and parallel-series systems. The developed method is used to analyze the fuzzy reliability of a computer system. Next, by generalizing the idea of trapezoidal vague sets [54] to interval valued trapezoidal vague sets, a method is introduced for analyzing the fuzzy reliability of various systems. Moreover, the method is applied to analyze the fuzzy reliability of a marine power plant. In Chapter 5, we have introduced the concept of L-R type triangular and L-R type interval valued triangular vague sets. Using (the weakest t-norm) — based arithmetic operations on these sets, we have further analyzed the fuzzy reliability of series and parallel systems. Moreover by taking case study of an electric robot, we have shown that our proposed method gives the exact solution for L-R type triangular vague sets while the existing methods yield approximate solutions. Further, through the example of basement flooding, it is shown that the results obtained by L-R type interval valued triangular vague sets are better than the results obtained using interval valued triangular vague sets [57]. In Chapter 6, we have further generalized the definitions of triangular vague set [19, 25, 26], trapezoidal vague set [54], interval valued triangular vague set [57] and interval valued trapezoidal vague set [55] to make the analysis more consistent and logical. By considering several cases it is shown that definitions of interval valued triangular vague set [57], interval valued trapezoidal vague set [55], triangular vague set [25, 26], trapezoidal vague set [54], triangular fuzzy number [95] and trapezoidal fuzzy number [95] are the particular cases of the definitions introduced in this chapter. Further, the fuzzy reliability of radar warning receiver is analyzed by the method proposed in this chapter. In Chapter 7, we have proposed algorithms to perform arithmetic operations between different types of vague sets and interval valued vague sets. The study of such operations is more flexible than arithmetic operations between same type of vague sets. We have also proposed an algorithm to analyze the fuzzy reliability of various systems. Finally, in Chapter 8, based on the present study, conclusions are drawn and future extensions of the research work in this direction are suggested.