Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

2025

Abstract

Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment with neutrosophic theory. Results show that K-Means uniquely achieves true independence of T, I, and F components—a key neutrosophic principle—yielding a T+I+F sum of 0.639, unlike the fuzzy-based methods whose sums exceed one. The method demonstrates a mean indeterminacy of 0.348 (SD = 0.237), combining theoretical soundness with adaptability to data structure. In contrast, model-based methods are computationally efficient but data-agnostic, while KDE is highly sensitive to density variations. Overall, the K-Means clustering approach provides a stable, interpretable, and reproducible framework for uncertainty quantification, representing a significant advancement in neutrosophic data transformation and analysis.

Keywords

Neutrosophic Logic, Neutrosophication, K-Means Clustering, Membership Functions, Uncertainty Quantification, Data Mining, Medical Informatics

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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