Advanced Risk-Averse Diagnosis of Diabetes Mellitus via Parameterized Asymmetric Spherical Fuzzy Similarity Measures with Log-Exp Dual Penalization

Abstract

Diabetes Mellitus has become a massive global health crisis, and it is estimated that 700 million people will be affected by 2030. The biggest problem right now is that our old testing tools depend on very strict “yes or no” limits. These tools often fail to understand “borderline” cases where symptoms are blurry or uncertain. In this paper, we introduce a new parameterized asymmetric similarity method based on Spherical Fuzzy Sets (SFS). Compared to older methods, SFS gives us more mathematical space to model uncertainty. We also introduce a “Log-Exp” dual penalization framework to grade these risks. The Exponential part gives a heavy penalty for missing serious risks that could put a patient’s life in danger (False Negatives) and the Logarithmic part gives a light penalty for extra symptoms that might not be as critical. To prove this works, we investigate some characteristics showing it is reliable and accurate. The model is tested on the “Pima Indians Diabetes Dataset” and the efficiency of the method in the diagnosis of borderline cases has been observed. Essentially, this work bridges the gap between complex mathematics and real-life medical diagnosis, making it easier to catch the disease early.