Stackelberg solutions for fuzzy random two‐level linear programming through level sets and fractile criterion optimization

This paper considers Stackelberg solutions for two‐level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two‐level linear programming problem, an α‐stochastic two‐level linear programming problem is defined through the introduction of α‐level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α‐stochastic two‐level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two‐level programming problem can be reduced to a deterministic two‐level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method.