Entropies of uncertain random variables are introduced to provide some kinds of quantitative measurement of the uncertainty. In chance theory, a concept of entropy for uncertain random variables has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain random variables. For solving this problem, this paper firstly define the elliptic e...

In many cases, human uncertainty and objective randomness simultaneously appear in a system. In order to describe this phenomena, this paper presents a new concept of uncertain random variable. To measure uncertain random events, this paper also combines probability measure and uncertain measure into a chance measure. Based on the tool of chance measure, the concepts of chance distribution, exp...

In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level ...

When performing a human health risk assessment using probabilistic methods, risk assessors need a way to distinguish, analyze, and visualize both the variability and the uncertainty in a quantity. As described by many previous authors, first-order random variables represent variability, i.e., the heterogeneity or diversity in a well-characterized population which is usually not reducible throug...