A possibilistc linear program is equivalent to a stochastic linear program in a special case

In this paper, the authors discuss an equivalent condition between a possibilistic linear programming problem with a quadratic membership function and a stochastic linear programming problem with a multivariate normal distribution. First, the possibilistic linear programming problem is formulated as a usual mathematical programming problem based on maximizing the necessity measure. Next, the stochastic linear programming problem is formulated as a visual mathematical programming problem by introducing the flexible programming approach. Since these two formulated programming problems are similar in their forms, an equivalent condition between these problems is given. Lastly, the equivalence is examined from a geometric viewpoint.