Volume 5 , Issue 2 , PP: 22–31, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Abd-Alrida Basheer 1 *
Doi: https://doi.org/10.54216/NIF.050203
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.
Dempster-Shafer evidence theory , Neutrosophic sets , Basic probability assignment , Information fusion , Conflict redistribution , Belief function , Pignistic probability , Water quality , Multi-source reasoning
[1] Chai, J. S., Selvachandran, G., Smarandache, F., Gerogiannis, V. C., Son, L. H., Bui, Q.-T., & Vo, B. (2021). New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems. Complex & Intelligent Systems, 7(2), 703–723. https://doi.org/10.1007/s40747-020-00220 w.
[2] Garg, H., & Nancy. (2020). Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure. AIMS Mathematics, 5(3), 2671–2693. https://doi.org/10.3934/math.2020173.
[3] Patel, A. (2021). Water quality dataset. Kaggle. https://www.kaggle.com/datasets/mssmartypants/ water-quality
[4] Qin, M., Tang, Y., & Wen, J. (2020). An improved total uncertainty measure in the evidence theory and its application in decision making. Entropy, 22(4), Article 487. https://doi.org/10.3390/e22040487.
[5] Shafer, G. (1976). A mathematical theory of evidence. Princeton University Press.
[6] Smarandache, F. (1998). Neutrosophy: Neutrosophic probability, set, and logic. American Research Press.
[7] Tang, Y., Tan, S., & Zhou, D. (2023). An improved failure mode and effects analysis method using belief Jensen-Shannon divergence and entropy measure in the evidence theory. Arabian Journal for Science and Engineering, 48, 7163–7176. https://doi.org/10.1007/s13369-022-07560-4.
[8] Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multistructure, 4, 410–413.
[9] Wu, L., Tang, Y., Zhang, L., & Huang, Y. (2023). Uncertainty management in assessment of FMEA expert based on negation information and belief entropy. Entropy, 25(5), Article 800. https://doi.org/10.3390/e25050800.
[10] Xiao, F. (2023). GEJS: A generalized evidential divergence measure for multisource informa-tion fusion. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 53(4), 2246–2258. https://doi.org/10.1109/TSMC.2022.3219498.
[11] Zhang, Z., Wang, H., Zhang, J., & Jiang, W. (2023). A new correlation measure for belief functions and their application in data fusion. Entropy, 25(6), Article 925. https://doi.org/10.3390/e25060925.
