Generalization of Trapezoidal Vague Set and Its Use for Analyzing the Fuzzy System Reliability

In this paper, definition of trapezoidal vague set (A. Kumar et al.) is generalized and by considering several cases it is shown that definitions of triangular vague set (S.M. Chen, 1997), trapezoidal vague set (A. Kumar et al.), triangular fuzzy number (G.J. Klir and B. Yuan, 1995), (H-J. Zimmermann, 1996) and trapezoidal fuzzy number (G.J. Klir and B. Yuan, 1995), (H-J. Zimmermann, 1996) are the particular cases of the definition of trapezoidal vague set introduced in this paper. Also arithmetic operations between two trapezoidal vague sets are introduced. Further new methods are developed for analyzing the fuzzy reliability of series and parallel systems. The developed methods are applied to analyze the fuzzy reliability of a radar warning receiver.