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

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 α‐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.