Application of Hexagonal Fuzzy Soft Matrices in The Diagnosis of Respiratory Tract Infections, Common Cold, and Pharyngitis

Hexagonal fuzzy numbers are an extension of pentagonal fuzzy numbers that allow a more flexible representation of uncertainty through asymmetric membership functions. In medical diagnosis, symptom intensity and patient conditions are often subjective and imprecise, making classical fuzzy representations insufficient. This paper proposes a hexagonal fuzzy soft matrix–based diagnostic model for respiratory tract infections, common cold, and pharyngitis. The novelty of this study lies in integrating hexagonal fuzzy number arithmetic with fuzzy soft matrix modeling, incorporating error variables to represent subjective uncertainty, and applying the model directly to medical diagnostic scoring. Interview and observation data are first transformed into numerical intervals and then mapped into hexagonal fuzzy numbers. These data are modeled as hexagonal fuzzy soft sets and represented in matrix form to compute diagnostic scores. The results show that the proposed approach can distinguish diseases with overlapping symptoms more sensitively than conventional fuzzy soft matrix methods, even under uncertain and limited data conditions.