Mean Value and Variance of Fuzzy Random Variables by Evaluation Measures

Abstract

This paper discusses an evaluation method of fuzzy numbers/fuzzy random variables by mean values and variance defined by fuzzy measures, and the method is applicable to decision making with both randomness and fuzziness. Next, we compare several possible approaches regarding variances by examining them for some fuzzy random variables with values at triangle-type fuzzy numbers. We find the method with lambda-mean functions has proper properties, and we derive fundamental properties regarding the variance and the corresponding co-variance and correlation. Formulae are given to apply the results to triangle-type fuzzy numbers, trapezoidal-type fuzzy numbers, and some types of fuzzy random variables