Modeling Uncertainty Using Set-Valued Random Variables

摘要

Set-valued random variable is defined as a mapping from a probability space to a collection of compact subsets of real line. The purpose of this paper is to provide the theoretical foundation of mathematical programming with set-valued random variables coefficients. First, the concepts of set-valued random variable and set-valued random vector are defined, their.relation and the function of set-valued variables are discussed. Then the belief, plausibility and confidence measures of a random set event are presented and the duality among thenr is proved. After that, three kinds of expected value operators of a set-valued random variable are proposed and the linearity of the operators is proved. Finally, we build three classes of set-valued random programming models by using the expected valued operators and the chance measures.