The foundation of handling uncertainty in real-world applications began in 1965 when Zadeh introduced Fuzzy Set Theory [1]. To address situations where the membership function itself is uncertain and cannot be expressed as a crisp value, the concept of Interval-Valued Fuzzy Sets was developed. Later, in 1986, Atanassov [2] extended this field by introducing Intuitionistic Fuzzy Sets (IFS), which incorporate both truth-membership and falsity-membership degrees. Samuel and Narmadhagnanam [3] developed tangent inverse distance and sine similarity measures for IFS to use in clinical diagnostics. Similarly, Rajkalpana et al. [4] utilized IFS and its operators for medical applications. Kozae et al. [5] applied IFS to COVID-19 diagnosis and determination. Shinoj and John [6] merged fuzzy multi-sets with IFS to create Intuitionistic Fuzzy Multi-Sets (IFMS). Rajarajeswari and Uma [7], [8] proposed various methodologies within IFMS, while Samuel and Narmadhagnanam [9] introduced sine inverse distance measures for IFMS, applying them to medical diagnostics. Eventually, IFS was further extended into Interval-Valued IFS to capture broader ranges of uncertainty. While intuitionistic and interval-valued IFS successfully manage incomplete data, they fail to process indeterminate and inconsistent information commonly found in real-world belief systems. To overcome this limitation, Smarandache [10] introduced Neutrosophic Sets (NS) from a philosophical perspective, capable of handling uncertain, imprecise, incomplete, and inconsistent data. Concurrently, Pawlak introduced Rough Set (RS) Theory [11] as a mathematical tool to model incomplete information using equivalence relations to establish lower and upper approximations. Over time, researchers merged these distinct frameworks: Nanda and Majumdar [12] studied Fuzzy RS. Broumi et al. [13] introduced Rough NS, which were later expanded with cosine and cotangent similarity measures by Pramanik and Mondal [14], [15], and correlation coefficients by Pramanik et al. [16]. Samuel and Narmadhagnanam [17–20] developed several rough neutrosophic methods specifically tailored for medical diagnosis. Zheng et al. [21] introduced a multi-granularity variable precision neutrosophic RS model featuring three distinct strategies for group decision-making. NS have been extensively adopted in decision-making and optimization [22–27]. Notably, Wang et al. [28] introduced Single-Valued Neutrosophic Sets (SVNS), prompting a wave of specialized research: Majumdar and Samanta [29] proposed similarity and entropy measures, while Ye [30] introduced a cotangent similarity measure. Ye et al. [31] also established correlation coefficients for both single-valued and interval-valued neutrosophic environments. New distance and similarity metrics were developed by Garg and Nancy [32], as well as Chai et al. [33]. Narmadhagnanam and Samuel [34], [35] introduced sine exponential measures and tan-log distances. Broumi et al. [36] introduced single-valued (2N+1)-sided and (2N)-sided polygonal neutrosophic numbers. Li et al. [37] developed a slope stability assessment approach using arctangent and tangent similarity measures of neutrosophic numbers. Imran et al. [38] designed a multi-attribute decision-making system using a single-valued neutrosophic hesitant fuzzy Aczel-Alsina aggregation operator. Byeon et al. [39] suggested an unsupervised SVNS approach for cloud clustering. To track multiple occurrences of elements, Ye and Ye [40] formulated Single-Valued Neutrosophic Multi-Sets. Samuel and Narmadhagnanam [41] then established a cosine exponential distance for these multi-sets to assist in medical diagnostics. In 2013, Smarandache [42] generalized these concepts into n-Valued Refined Neutrosophic Logic, breaking down the standard components into sub-components. This gave rise to Neutrosophic Refined Sets (NRS), generalizing both fuzzy and IFMS. Broumi and Smarandache [43] extended Ye’s [44] improved cosine similarity measure to NRS. Samuel and Narmadhagnanam [45], [46] designed multiple NRS methods for clinical diagnosis. Zhao and Ye [47] implemented a Multi-Criteria Group Decision-Making (MCGDM) model using a weighted hyperbolic sine similarity measure on neutrosophic multivalued sets for assessing teacher quality. Hemabala et al. [48] evaluated medical diagnoses utilizing refined neutrosophic fuzzy logic. Wang et al. [49] introduced Interval Neutrosophic Sets (INS) to allow membership degrees to be represented as intervals rather than crisp values. This framework evolved through several key contributions: Ulucay [50] explored concepts regarding interval-valued refined NS, and later [51] introduced hybrid distance-based similarity measures for n-valued neutrosophic trapezoidal numbers. Pourersmaeil et al. [52] designed a parametric scoring function for multi-criteria decision-making. Liu et al. [53] engineered a similarity measure for INS to optimize resource offloading in edge computing. Hema et al. [54] formulated a novel approach within a plithogenic interval-valued neutrosophic environment. Saqlain et al. [55] utilized a neutrosophic linguistic valued hypersoft set for medical treatment and diagnosis. Broumi et al. [56] generalized n-valued

methodologies within this domain, successfully applying them to clinical diagnostics. To deliver a more dependable and accurate medical diagnostic tool, this paper introduces a novel, streamlined and highly precise approach based on SVNS.

The remainder of this article is organized as follows. Section 2 Reviews essential preliminary concepts. Section 3 Defines the proposed concept and analyzes its core properties. Section 4, 5, and 6 Present the clinical assessment framework, operational procedure, and a hypothetical medical diagnosis case study, respectively. Section 7 Outlines the significance statements of the research. Section 8 Concludes the paper with final remarks.

log distance is defined as

Proposition 1.

II.

Proof: 1) For SVNS, it is evident that the truth-membership function, indeterminacy-membership function and falsity-membership function are within [0,1]. Hence, . 2) We are aware of that

Hence,

and

I. C represents the classifications of illnesses: {Diabetes Mellitus, Dengue fever, Pulmonary Tuberculosis}.

{Amit, Jeyanthinathar, Janardanan}.

{Body Temperature, Fatigue, Weight loss, Loss of appetite, Malaise}.

let E1 denote the single-valued neutrosophic relation mapping those indicators to the specific patient cohort and Let E2 denote the single-valued neutrosophic relation mapping the disease classifications to the clinical indicators, and

I. Indicator determination: Identifying and evaluating the relevant clinical symptoms.

II. Knowledge modeling: Constructing a scientific framework utilizing SVNS.

III. Diagnostic assessment: Evaluating the data through the newly developed processing technique.

Step 1. Table 1 details a cohort of patients exhibiting a particular pathology, mapped against a specific set of clinical indications, denoted as E1.

Step 2. Table 2 outlines the correlation between the specified set of clinical indications and the disease classifications, denoted as E2.

Step 3. By evaluating the data from Tables 1 and 2, the calculation E3 is derived and recorded in Table 3. To determine the likelihood that a specific patient cohort is affected by a particular disease classification, the lowest value within each row was selected.

Table 3 indicates that Amit is suffering from Dengue fever, Jeyanthinathar and Janardanan are experiencing Diabetes Mellitus.

The findings of this study enable the precise identification of the specific illnesses affecting the participating individuals. Because the employed methodology is free from the constraints common to alternative approaches, it expands beyond clinical diagnostics to offer foundational insights for novel theories in fields such as pattern recognition and image processing.

This study investigated how a specific group of individuals with a particular pathology relates to the signs and classification of their illness. To determine which specific disease likely affected them, we utilized the "sin – log distance" technique. Because this method is reliable and accurate, it provides an efficient way to manage complex medical diagnostic challenges. Ultimately, this approach improves diagnostic precision, allowing it to overcome the limitations and drawbacks found in previous research.

We highly appreciate the constructive feedback provided by the anonymous reviewers, as their insights have significantly enhanced the overall quality of this work.

There was no outside support for this study.

The writers say they have no competing interests.