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Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations |
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| Authors: | Dug Hun Hong and Hae Young Do |
| Affiliation: | a School of Mechanical and Automative Engineering, Catholic University of Taegu-Hyosung, Kyungbuk 712-702, South Korea b Department of Statistics, Catholic University of Taegu-Hyosung, Kyungbuk 712-702, South Korea |
| 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 Tω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show Tω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply Tω-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. |
| Keywords: | Fuzzy number Fuzzy system reliability Possibility distribution sup-t-norm convolution Interval arithmetic |
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