Type-2 Trapezoidal Pythagorean fuzzy number with novel entropy measure and aggregation operators extended to MCDM

Abstract

The human immune response to the influenza virus involves complex interactions that require advanced decision-making tools to guide effective therapeutic interventions. This study introduces a novel decision-making framework grounded in Type-2 Trapezoidal Pythagorean Fuzzy Sets (T2TrPyFS), augmented with a newly developed entropy measure and enhanced aggregation operators, to improve the precision of Multi-Criteria Decision-Making (MCDM) processes. The model evaluates key factors affecting immune response, including viral traits, host characteristics, and treatment efficacy. To prioritize these factors, we applied the Combinative Distanceased Assessment (CODAS) and Complex Proportional Assessment (COPRAS) methods. In the CODAS analysis, risk factor ${\mathfrak{R}}_{24}$ (heavy virus strain in the body) received the highest score of 12.9631, while in COPRAS, ${\mathfrak{R}}_{31}$ (direct contact) ranked highest with a score of 100. A fuzzy inference-based ranking approach confirmed the prominence of ${\mathfrak{R}}_{24}$ as the most critical factor across methods. Additionally, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), and Weighted Aggregated Sum Product Assessment (WASPAS) methods were integrated to reinforce the analysis. The top-ranked factor identified was ${\mathfrak{R}}_{24}$ in TOPSIS (0.8129), VIKOR (0.0392), and CODAS (12.9631), while COPRAS highlighted ${\mathfrak{R}}_{31}$, and WASPAS identified "headache" as the leading factor (0.00517). Final rankings using fuzzy inference once again confirmed ${\mathfrak{R}}_{24}$ as the most influential risk factor. A comprehensive sensitivity analysis was conducted to evaluate the robustness of the results under varying weights and uncertainties. The findings demonstrate the adaptability, stability, and effectiveness of the proposed fuzzy MCDM framework for supporting personalized and targeted influenza treatment strategies.