Fermatean fuzzy distance model for the prediction of glaucoma risk based on clinical data via MCDM methodology

Abstract

Glaucoma is one such major cause of irreversible blindness, yet early diagnosis and constant monitoring remain some of the major clinical challenges due to variability in ocular parameters and patient response. In this paper, a Fermatean Fuzzy Distance Model is developed to quantify and interpret glaucomatous neuropathy progression through multi-parametric ophthalmic indicators. Each patient’s profile-given by IOP, CCT, C/D, RNFL thickness, and age-is translated into Fermatean fuzzy triples, thereby encapsulating supporting, contradicting, and uncertain evidence for disease classification. Clinical data and anonymised patient records from the Ophthalmology Department were procured from the Optometry Department of the Abia State Ministry of Health between 2021 and 2024. The dataset contained clinically verified readings collected from confirmed cases of glaucoma and non-glaucoma, under due ethical clearance and according to institutional guidelines for secondary data use. Using established Fermatean Fuzzy Distance Models, a few comparative studies are performed to determine the closeness of various patient conditions to positive and negative ideal states. The results obtained show a consistent ranking scheme according to the physiological progression of the disease-from controlled intraocular pressure with preserved optic nerve function to advanced optic neuropathy. The new distance function based on logarithms is given greater discriminatory power in differentiating between borderline cases of glaucoma and those with advancing glaucoma, providing a smoother transition between disease stages. On the other hand, interpretability analysis uncovered that the proposed Fermatean Fuzzy Distance Model allows a transparent ranking system from a clinical perspective. Therefore, the proposed approach offers an interpretable, mathematically sound framework of glaucoma risk assessment that, in turn, supports ophthalmologists in monitoring diseases on a patient basis and making appropriate decisions.