A Variable-Indeterminacy Weighted Correlation Framework in Neutrosophic Statistics

Abstract

Correlation analysis under uncertain and imperfect information remains a fundamental challenge in statistical modeling. Although neutrosophic statistics provides a flexible framework for handling truth, falsity, and indeterminacy simultaneously, most existing neutrosophic correlation measures treat the indeterminacy component as uniform across observations. Such an assumption may oversimplify real data, where uncertainty often varies due to measurement errors, subjective assessments, or incomplete knowledge. In this paper, a weighted neutrosophic correlation framework with observation-dependent indeterminacy is developed. The proposed model allows each data point to possess its own indeterminacy level and incorporates weighting parameters to reflect the relative reliability or importance of observations. Based on these considerations, a new weighted neutrosophic correlation coefficient is formulated using neutrosophic means, variances, and covariance. Fundamental statistical properties of the proposed coefficient, including boundedness, symmetry, and invariance under linear transformations, are rigorously established. A detailed numerical illustration is provided to demonstrate the computational procedure and to show how variable indeterminacy and weighting influence the strength of association between variables. The proposed approach offers a more realistic and adaptable tool for analyzing relationships in uncertain environments and may serve as a useful foundation for further developments in neutrosophic data analysis and decision-making applications.