Generalization of Fuzzy Sets and its Use for Analyzing the Fuzzy System Reliability

Abstract

In this paper, the concept of vague sets is extended by idea of interval valued vague sets. Also we have introduced: definition of interval valued triangular vague set and arithmetic operations between two interval valued triangular vague sets. Further, a new method has been developed for analyzing the fuzzy system reliability of a series and parallel system using interval valued triangular vague sets, where the reliability of each component of a system is represented by an interval valued triangular vague set defined in the universe of discourse [0,1]. The developed method has been used to analyze the fuzzy reliability of a computer system. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison to the method given by Chen [14]. The major advantage of the proposed approach (the concept of interval valued vague sets) over the existing approaches [7, 8, 14] is that the proposed approach separates the positive and negative evidence for the membership of an element in a set. Also in the proposed approach the values of the membership and non-membership of an element in a set are intervals instead of a single real number.