An In-Depth Analysis of the Neutrosophic Exponential Distance Measure: Properties, Applications, and a Case Study in Medical Diagnosis

Abstract

This research article provides an exhaustive analysis of a novel neutrosophic exponential distance measure, meticulously examining its formal definition, axiomatic properties, and practical applicability. Building upon the foundational principles of neutrosophic sets, which adeptly handle uncertainty, indeterminacy, and inconsistency in real-world data, this study delves into the mathematical validity of the proposed measure, critically assessing its non-negativity, identity of indiscernibles, and symmetry. A particular focus is placed on a rigorous re-evaluation of its triangle inequality property, identifying a critical mathematical nuance that distinguishes it as a "distance-like" measure rather than a strict metric. The article further contextualizes this measure through a comparative discussion with established neutrosophic distance metrics, highlighting its unique characteristics and potential advantages in specific scenarios. To demonstrate its utility, a detailed application case study in medical diagnosis is presented, illustrating how the measure can effectively quantify dissimilarities between patient symptom profiles and known disease patterns, thereby aiding in clinical decision-making under inherent imprecision. This work contributes to the theoretical understanding and practical implementation of neutrosophic distance measures, offering insights into their strengths, limitations, and future research directions.