Independent fuzzy random variables and their application

Abstract

In this paper, we define the probability measure P ̃ ( X ̃ (w 1),…, X̃ n(w n)) of fuzzy sets X ̃ 1 (w 1),…, X ̃ n(w n) and induce some properties of it. We also compare our probability measure with that of Zadeh (1968). Moreover, we have different results about the independence which derive from these two probability measures. Under our probability measure, we also define MLE to estimate unknown parameter. We also provide two examples to demonstrate how to use MLE to estimate unknown parameter.