On solutions and distribution problems of the linear programming with fuzzy random variable coefficients

Abstract

This paper studies the solution method and distribution problems for two kinds of linear programming with fuzzy random variable coefficients. Some concepts of solutions (for example, the fuzzy (pseudo-) random optimization solution) are introduced for these new programming problems. We prove some equivalent theorems that transform the fuzzy random programming problems into a series of random programming problems. By using the simplex method of linear programming with random variable coefficients, we give the solution method of linear programming with fuzzy random variable coefficients. The formulas of probability distribution function, projective distribution function and expectation on these new programmings are presented.