Fully Hesitant Fuzzy Bilevel Linear Programming and Its Application to Quantum Communication Resource Allocation

The problem of bilevel decision-making under multi-expert uncertain information is addressed in this paper. Traditional fuzzy bilevel models are unable to accurately quantify expert consensus and capture evaluation hesitation. To overcome these limitations, a fully hesitant fuzzy bilevel linear programming model is proposed, in which all coefficients and decision variables are characterized by hesitant fuzzy numbers. By virtue of (α,k)-cuts, the original model is equivalently transformed into an interval-valued bilevel programming problem and further decomposed into best–best and worst–worst sub-models to derive the upper and lower bounds of optimal solutions. Under the Slater constraint qualification, Karush–Kuhn–Tucker (KKT) conditions are adopted to convert the two sub-models into single-level mathematical programs with complementarity constraints (MPCCs), thereby enabling efficient model solving. The proposed method is applied to the resource allocation problem in quantum communication networks. The numerical results demonstrate that the optimal solution interval converges to a unique core value as the membership-level α increases, while a larger consensus parameter k reduces the fuzzy support set without altering the core solution.