A possibilistic linear program is equivalent to a stochastic linear program in a special case. (English) Zbl 0856.90131

Summary: We 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 usual 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.


90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C15 Stochastic programming
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