A Neutrosophic Dempster-Shafer Evidence Fusion Framework with
Conflict-Redistribution and Pignistic Decision for Multi-Source Water
Potability Classification
Abd-Alrida Basheer1,*
1Imam Kadhum College, Iraq
Email: basheerabdalrida66n@gmail.com
Abstract
Assessing drinking water safety requires integrating evidence from nine independent physicochemical measurements—pH,
hardness, total dissolved solids, chloramines, sulfate, conductivity, organic carbon, trihalomethanes, and turbidity—each of
which independently provides only weak discriminative power, so that conflicting evidence and high indetermi-nacy are
structural features of the problem rather than anomalies. This paper develops a Neutrosophic Dempster-Shafer Evidence
Theory (N-DSET) framework in which each measurement is treated as an independent evidence source mod-elled by a
Neutrosophic Basic Probability Assignment (NBPA) constructed from class-conditional kernel densities. Evidence is fused
through a modified Dempster combination rule that redirects inter-source conflict mass into the neutrosophic
indeterminacy component rather than discarding it via normalisation—preserving epistemic information about
measurement disagreement throughout the reasoning chain. Source reliability weights are derived from Deng entropy, and
the final binary decision uses the pignistic probability transformation. Experiments on the Kaggle Water Quality Dataset (𝑛
= 3,276, Kaggle 2021) yield an AUC of 0.618 under ten-fold cross-validation, exceeding all five supervised baselines
including Logistic Regression, Gradient Boosting Trees, and AdaBoost, whose AUC values lie in [0.521, 0.552] on this
inherently ambiguous dataset. A sequential waterfall analysis demonstrates monotonically increasing AUC as each
evidence source is successively fused, confirming the incremental value of each measure-ment. The belief-plausibility
interval [𝐵𝑒𝑙(𝑃), 𝑃𝑙(𝑃)] provides a rigorous geometric characterisation of the three-way decision regions (Positive,
Negative, Boundary), and its width—approximately 0.83—quantifies the structural indeter-minacy inherent in the
potability classification task. Mathematical properties of the N-DSET operator—commutativity, associativity, convergence
of conflict mass under growing evidence sets, and the equivalence of the combined pignistic probability to Bayesian
posterior when no conflict is present—are formally established.
Keywords: Dempster-Shafer evidence theory; Neutrosophic sets; Basic probability assignment; Information fusion;
Conflict redistribution; Belief function; Pignistic probability; Water quality; Multi-source reasoning