A Hybrid Approach to Managing Uncertainty in Decision-Making: The OrdPA-F Method for Pythagorean Fuzzy Rough Numbers and MARCOS

Abstract

In this paper, we introduce a novel hybrid Multi-Criteria Decision-Making (MCDM) model that integrates Pythagorean fuzzy sets and rough numbers to more effectively manage various uncertainties inherent in complex decision problems. To overcome the limitations of traditional weight determination methods, we propose a new model called Ordinal Preference Analysis under Fuzziness (OrdPA-F). This method calculates robust criteria weights using only simple ordinal rankings from experts, offering a practical advantage over data-intensive methods like entropy and cognitively demanding techniques like Analytic Hierarchy Process (AHP). The OrdPA-F framework uniquely integrates subjective expert preferences with an objective quantitative measure of overall ranks. These derived weights are subsequently utilized within a Pythagorean Fuzzy Rough Number (PFRN)-based Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) model, enhanced by Dombi aggregation operators to accurately capture nonlinear relationships between criteria. A comprehensive case study on hypertension risk management demonstrates the practical efficacy and specific results of the proposed model. Our findings systematically rank elevated systolic blood pressure and high cholesterol level as the two most critical risk factors, with lifestyle modification identified as the most effective mitigation strategy. A comparative analysis with established methods (Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and VIseKriterijumska Optimizacija I Kompromisno Resenjee (VIKOR)) quantitatively confirms the superiority of our framework, showing a 12% improvement in ranking stability and an 8% higher insensitivity to weight perturbations. These results demonstrate that the model provides a theoretically sound approach and delivers a reliable, robust, and practical decision support tool for healthcare diagnostics, enabling medical professionals to prioritize interventions with greater confidence.