A Study on Fuzzy Random Linear Programming Problems Based on Possibility and Necessity Measures

In this paper, we deal with linear programming problems with fuzzy random variable coefficients and propose two decision making models based on possibility and necessity measures. One is the expectation optimization model, which is to maximize the expectation of degrees of possibility or necessity that the objective function value satisfies with a fuzzy goal given by a decision maker. The other is the variance minimization model, which is to minimize the variance of the degree. We show that the formulated problems based on the expectation optimization model and on the variance minimization model are transformed into a linear fractional programming problem and a convex quadratic programming problem, respectively and that optimal solutions of these problems are obtained by using conventional mathematical programming techniques.