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...

Introduction: A chance constrained optimization problem involves constraints with stochastic data that are required to be satisfied with a pre-specified probability. When the underlying distribution of the stochastic data is not known precisely, an often used model is to require the chance constraints to hold for all distributions in a given family. Such a problem is known as a distributionally...

Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance cons...