The possibility neutrosophic hypersoft set (pNHs-set) is a generalized version of the possibility neutrosophic soft set (pNs-set). It tackles the limitations of the pNs-set regarding the use of the multi-argument approximate function. This function maps sub-parametric tuples to a power set of the universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. This makes the decision-making process more flexible and reliable. In this study, after characterizing some elementary notions and algebraic operations of the pNHs-set, Sanchez’s method (a classical approach for medical diagnosis) is modified under the pNHs-set environment. A modified algorithm is proposed for the medical diagnosis of heart diseases by integrating the concept of the pNHs-set and the modified Sanchez’s method. The authenticity of the proposed algorithm is evaluated through its implementation in a real-world scenario with real data from the Cleveland data set for heart diseases. The beneficial aspects of the proposed approach are evaluated through a structural comparison with some pertinent existing approaches.

Chronic diseases are the most severe health concern today, and heart disease is one of them. Coronary artery disease (CAD) affects blood flow to the heart, and it is the most common type of heart disease which causes a heart attack. High blood pressure, high cholesterol, and smoking significantly increase the risk of heart disease. To estimate the risk of heart disease is a complex process because it depends on various input parameters. The linear and analytical models failed due to their assumptions and limited dataset. The existing studies have used medical data for classification purposes, which help to identify the exact condition of the patient, but no one has developed any correlation equation which can be directly used to identify the patients. In this paper, mathematical models have been developed using the medical database of patients suffering from heart disease. Curve fitting and artificial neural network (ANN) have been applied to model the condition of patients to find out whether the patient is suffering from heart disease or not. The developed curve fitting model can identify the cardiac patient with accuracy, having a coefficient of determination (R²-value) of 0.6337 and mean absolute error (MAE) of 0.293 at a root mean square error (RMSE) of 0.3688, and the ANN-based model can identify the cardiac patient with accuracy having a coefficient of determination (R²-value) of 0.8491 and MAE of 0.20 at RMSE of 0.267, it has been found that ANN provides superior mathematical modeling than curve fitting method in identifying the heart disease patients. Medical professionals can utilize this model to identify heart patients without any angiography or computed tomography angiography test.