Frank-Driven Power Maclaurin Symmetric Mean Operators on p, qQuasirung Orthopair Fuzzy Sets: A Decision Framework for Emergency Helipad Site Selection in Disaster Relief

Abstract

Abstract

Picking a safe spot to land a rescue helicopter during a flood or earthquake is rarely a clean optimisation problem. Commanders weigh soil firmness against approach geometry, accessibility against wind exposure, and they do so under time pressure, with information that is partial, contradictory, and tinged with personal judgment. The recently introduced p, q-quasirung orthopair fuzzy set (p, q-QOFS) framework offers a flexible canvas for such ambiguity, since it decouples the exponents that govern membership and non-membership. In this work we extend that framework along two axes. First, we equip p, q-QOFSs with Frank operational laws, which give the decision maker an extra knob (the parameter τ) for tuning the steepness of aggregation. Second, we wed the Power Average—useful for damping outliers in expert opinions— with the Maclaurin Symmetric Mean (MSM), which captures interactions among k criteria at a time. The resulting family of four operators (PMSM, weighted PMSM, dual PMSM, weighted dual PMSM) is shown to be idempotent, monotonic, bounded and commutative. To reduce subjective bias when fixing criterion weights, we couple Shannon entropy with the CRITIC method. The framework is exercised on a fabricated but realistic case: choosing a helipad in a flood-affected basin from five candidate sites against six criteria. Numerical experiments, such as sensitivity sweeps over (p, q, τ, k), a 10,000- trial Monte Carlo perturbation, and a head-to-head comparison with eight published methods, indicate that the suggested scheme is robust, discriminative, and provides roughly a 9% improvement in rank-stability over its closest competitor.