Asian Research Journal of Mathematics

In this paper, we develop an analytical framework to identify the most significant core factor among a set of core factors by quantifying how severely the removal of each factor degrades probabilistic diagnostic performance. Although Jeevitha et al. identified the core factor set {F,L} for dengue diagnosis using attribute reduction through Nano-topology, their approach did not quantify the relative impact of each factor. Over a 15-patient dengue dataset, a Nano-topological space is constructed via Pawlak rough approximations; attribute reduction identifies Core = {F,L}; a classification tensor expressed in terms of topological approximations yields the F1 score as a Jaccard-like overlap and step-function AUC by the trapezoidal rule. Subsequently, we establish a Dirichlet–Beta conjugacy, through which the Bayesian posterior distribution is derived, enabling corrected uncertainty quantification for small-sample bias. Two ordinary least-squares (OLS) regression models—the penalty regression model and the confidence-degradation regression model—are then introduced to quantify the linear relationship between false-positive boundary contamination and diagnostic degradation. Removing LLBP inflates false positives from 1 to 3 at the optimal threshold α^∗ = 0.5, reducing Bayesian diagnostic confidence from 95.3% to 75.9%. The confidence-degradation regression C = 1.0553 − 0.0970 · FP achieves R2 = 0.991, and every comparative metric confirms LLBP to be approximately 2.20 times more hazardous than Fever. The proposed Nano-Topological–Bayesian framework provides a statistically credible and clinically interpretable tool for identifying the dominant core hazard factor in small-sample medical datasets, with LLBP confirmed as the critical hazardous attribute for dengue diagnosis.