Uncertain Random Programming With Non-monotone Functions

It is reasonable to assume that random variables and uncertain variables co-exist in a complex system. In order to deal with this type of complex system, Liu Y. proposed a concept of uncertain random variable which is a measurable function from a chance space to the set of real number. Base on chance theory, the independence of uncertain random variables is given and some properties are studied in this thesis.For a complex system with uncertain random variables, we need to use uncertain random programming to model. In fact, we already know that an uncertain random programming model can be converted to a crisp mathematical programming if all ob-jective and constraint functions are monotone with respect to the uncertain parameters. However, if they are non-monotone, the above results may be not true. For solving the non-monotone situation, this dissertation will build uncertain random expected value programming model and chance-constrained programming model with non-monotone functions, and uncertain random simulation are proposed.The contributions of this thesis are:· The independence of uncertain random variables is given and some properties are studied.· The chance distribution and expected value of function of uncertain random variables are studied.· Uncertain random expected value programming model and chance constrained programming model with non-monotone functions are established, and uncertain ran-dom simulations are proposed to solve the models.