任意有界论域的模糊变量转化成随机变量的方法

针对机械系统广义可靠性中极限状态方程的模糊参数向等价正态随机变量转化时其均值难以确定的问题,提出了一种将具有任意有界论域的模糊变量转化成随机变量的方法,以该法所得的随机变量的均值作为等价正态随机变量的均值,得到模糊变量的更为准确的等价正态随机变量表达式,使含有模糊参数机械系统可靠度能在正态空间内确定.并在算例中以水平截集法作为准确值,验证了该方法的准确性和简洁性.

Transformation fuzzy variable into equivalent normal random variables in context of fuzzy reliability

The present paper aims to introduce the author's new approach to determining the expected values of an equivalent normal random variable in transforming a fuzzy variable with an arbitrary universe of discourse into its equivalent normal random variable in a mechanical system. The approach, to some extent, consummates that the existing methods can only find out the variance for the equivalent normal random variable. Therefore, it is supposed to be established on the following two analytical theoretical proofs: (1) random entropy for an equivalent variable, gained by using our approach identically, equals to fuzzy entropy for a fuzzy variable to be transformed; (2)conventional reliability formula, in which an equivalent variable obtained from our approach, can be used as equivalents to fuzzy reliability formula, in which one of its uncertainty parameters, is a fuzzy variable to be transformed. The rationality of our approach is thus be proved by using well-established theory of fuzzy reliability, and is validated by using a well established Random Simulation Method, namely, random cut set method. Numerical examples help to validate the rationality and accuracy of our new approach.