Breast milk is the primary source of nutrition for infants, and its contamination with heavy metals poses a significant health risk. Mothers residing in polluted areas, particularly those with poor dietary habits, are more likely to have elevated heavy metal levels in their breast milk. Lahore, Pakistan, faces significant environmental contamination, making the assessment of heavy metal concentrations in breast milk crucial. This study addresses this concern by employing neutrosophic statistics, a method particularly well-suited to analyze imprecise and indeterminate data often encountered in environmental studies. The research aims to provide a more accurate and detailed understanding of heavy metal variation in breast milk, considering the inherent uncertainties associated with such measurements. This detailed analysis can contribute to identifying risk factors, improving public health strategies, and ultimately reducing the exposure of infants to hazardous substances. The impact of heavy metals like lead (Pb), mercury (Hg), and cadmium (Cd) on various organ systems (nervous system, kidneys, etc.) in infants highlights the critical nature of this research. The study's importance stems from the vulnerability of infants, the unique way metals distribute within milk fractions, and the prevalent practice of breastfeeding in Pakistan, often exceeding the WHO's recommended six months.

Existing literature documents the detrimental effects of heavy metal contamination on human health globally. Studies have explored the presence of heavy metals in various food sources and the consequences of long-term exposure. Previous research has also applied neutrosophic statistics to analyze imprecise data in various fields, including medicine and environmental science. While studies have investigated heavy metal concentrations in soil and the impact of environmental factors on human health in Pakistan, this study specifically focuses on heavy metal concentrations in breast milk within a specific region of Lahore using a neutrosophic statistical approach. The novelty lies in applying this relatively new statistical method to improve the accuracy and detail of analysis, especially when dealing with the inherent uncertainty of environmental sample data and the variability inherent in biological measurements.

This study involved the collection of 70 breast milk samples from lactating mothers aged 25-40 years in Lahore, Pakistan. Samples were collected at the end of the third lactation month and processed using established protocols involving the removal of organic components and dilution with distilled water before analysis. A Flame Atomic Absorption Spectrometer (FAAS) was used to measure the concentrations of lead (Pb) and mercury (Hg). The key innovation of this study was the application of neutrosophic statistics to analyze the obtained data. Unlike classical statistical methods that average interval data, resulting in the loss of information on data variability, the neutrosophic approach directly incorporates the indeterminacy inherent in interval measurements. The neutrosophic formulas used allow for the calculation of both determined and indeterminate components of heavy metal concentrations. A computational algorithm was developed to process the data using the neutrosophic approach. This algorithm involved several steps: obtaining the interval data, calculating the indeterminacy using a specific formula, applying the neutrosophic formula to calculate both determined and indeterminate values, and finally, generating graphical representations to visualize the results. These graphs allowed for a direct comparison between the neutrosophic and classical statistical analyses. The study explicitly defined the neutrosophic formula and its parameters for analyzing the heavy metal concentrations, emphasizing its extension from classical statistics by incorporating an indeterminacy interval. This interval reflects the uncertainty associated with the measurements. The study provides detailed explanation of the data collection and preprocessing steps, ensuring the reproducibility of the methodology.

The study's key findings are presented in Table 1, which compares the neutrosophic and classical analyses of lead (Pb) and mercury (Hg) concentrations in breast milk across different maternal age groups. The neutrosophic analysis provides interval values reflecting the uncertainty of the measurement, while the classical approach provides a single average value. The table demonstrates that the neutrosophic approach captures the variability within the data more effectively than the classical method. Figures 1 and 2 graphically illustrate the comparison of the neutrosophic and classical data for mercury and lead respectively, showcasing the superior adaptability of the neutrosophic approach for representing the data's variation. Table 2 provides a summary comparison of the classical and neutrosophic statistical approaches, highlighting the advantages of the neutrosophic method in handling imprecise data, specifically its ability to manage indeterminacy and its greater flexibility. Table 3 presents the raw collected data for lead and mercury in interval form for different age groups. The results demonstrate that the neutrosophic approach offers a more nuanced and accurate representation of the data by accounting for the indeterminacy. The data suggests that the concentrations of these heavy metals vary with age, with considerable individual variability within each age group. The figures reveal that the neutrosophic method provides a richer understanding of the data by showing the range of values instead of a single point estimate. The study also includes Figure 3, which illustrates the experimental setup, namely the use of a Flame Atomic Absorption Spectrometer for the collection and detection of heavy metals. Figure 4, the flowchart for the computational algorithm, outlines the step-by-step process for applying the neutrosophic statistical analysis to the obtained data. The presented results highlight the significance of using a method capable of handling the inherent uncertainty in environmental measurements.

The findings confirm the effectiveness of the neutrosophic approach in analyzing the imprecise data on heavy metal concentrations in breast milk. The comparison between the neutrosophic and classical methods demonstrates that the neutrosophic approach captures the inherent variability and uncertainty better than the classical approach, which simplifies the analysis and improves accuracy. The study's findings suggest elevated levels of Pb and Hg in breast milk, especially in mothers from industrial areas. This information has important implications for public health interventions aimed at reducing exposure to these toxic metals. The use of neutrosophic statistics provides a more complete picture of the data and helps inform decision-making regarding risk mitigation strategies. Further research could explore the correlation between heavy metal levels in breast milk and maternal dietary habits, environmental factors, and infant health outcomes. The method's applicability could be tested in other environmental monitoring contexts and potentially be adapted for different types of data analysis.

This study successfully applied neutrosophic statistics to analyze heavy metal concentrations in breast milk, demonstrating its superior adaptability compared to classical methods. The results highlight the significance of accounting for data uncertainty in environmental studies and provide a more comprehensive understanding of heavy metal variation in breast milk. The findings emphasize the need for further research to investigate the sources of contamination and develop targeted interventions to mitigate health risks. The neutrosophic approach has been shown to be a valuable tool for analyzing imprecise and indeterminate data in environmental health research.

The study is limited to the analysis of lead (Pb) and mercury (Hg) in breast milk and to a specific region of Lahore, Pakistan. The sample size, while sufficient for this study, might not be representative of the entire population of Lahore. The study did not explore the potential health effects of these heavy metals on infants. The generalizability of the findings is limited by the geographical specificity of the study area and the specific age range of the mothers included. The methodology is specific to interval data; it is not directly applicable to datasets lacking interval values. The current study only considered two heavy metals; expanding the analysis to include other heavy metals would provide a more complete picture.