A POSSIBILISTIC LINEAR PROGRAM IS EQUIVALENT TO A STOCHASTIC LINEAR PROGRAM IN A SPECIAL CASE

In this paper, we discuss an equivalent condition between a possibilis tic linear programming problem with a quadratic membership function an d a stochastic linear programming problem with a multivariate normal d istribution. First, the possibilistic linear programming problem is fo rmulated as a usual mathematical programming problem based on maximizi ng the necessity measure. Next, the stochastic linear programming prob lem is formulated as a usual mathematical programming problem by intro ducing the flexible programming approach. Since these two formulated p rogramming problems are similar in their forms, an equivalent conditio n between these problems is given. Lastly, the equivalence is examined from a geometric viewpoint.