Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

Abstract

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T ω -based addition preserves the shape of L- R type fuzzy numbers. In this paper, we show T ω -based multiplication also preserves the shape of L- R type fuzzy numbers. We then apply T ω -based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L- R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.