An approach for linear programming under randomness and fuzziness: a case of discrete random variables with fuzzy probabilities

Abstract

This paper presents a new approach for solving stochastic fuzzy linear programming problems. The random variables in the constraints and in the objective function are discrete with triangular fuzzy probabilities. The D-cut method is applied to the triangular membership functions of the fuzzy probabilities. For the constraints, the chance-constrained approach is utilised, whether according to strict dominance relation or dominance relation. The mean-variance criterion is exploited in the objective function, whereas four different cases are considered. The model, for the general case, which takes the form of mixed zero-one non-linear programme, is illustrated by a numerical example.