Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach

In this paper, a multi-choice stochastic bi-level programming problem (mcsblpp) is considered where all the parameters of constraints are followed by normal distribution. the cost coefficients of the objective functions are multi-choice types. at first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of decision makers(dms). then the transformed problem is considered as a deterministic multichoice bi-level programming problem. finally, a numerical example is presented to illustrate the usefulness of the paper.