Biuncertain Variables And Biuncertain Programming

In some multiple indeterminate phenomena, birandom has gained many research, while biuncertain phenomenon exists in the real world. In this thesis, on the basis of uncertainty theory, we introduce a new concept, namely biuncertain variable. An uncertain variable is a measurable function from an uncertainty space to the set of real number, and a biuncertain variable is a measurable function from an uncertainty space to the set of uncertain variables. This thesis puts forward the concept of biuncertain variables, then studies the properties of biuncertain variables. This thesis presents a concept of chance measure in order to measure biuncertain events, and also give a definition of chance distribution function of biuncertain variable. What’s more, the concept of expected value of biuncertain variable is proposed, and the thesis also study the linearity of expected value operator of biuncertain variable.For an optimization, if the system contains biuncertain variables, the previous optimization model will no longer apply, and so as to solve this problem, biuncertain expected value programming and chance-constrained programming are presented. For solving this model efficiently, biuncertain simulation to calculate the expected value is designed and illustrated by several numerical examples.