Pythagorean Neutrosophic Framework and Its Application to Correlation-Based Threat Identification

Abstract

In intelligence analysis, surveillance systems, and threat assessments, usual models that rely on discrete mathematics often do not capture the ambiguity in the information well. Uncertainty, incompleteness, and inconsistency are common in intelligence analysis, surveillance systems, and threat assessment, where traditional mathematical models are often unable to adequately describe the ambiguity in the information. In this paper, a Pythagorean neutrosophic framework called Pythagorean Neutrosophic Framework (PNF), is developed for threat identification in uncertain environment, based on the correlation features. This proposed framework will integrate the expressive power of Pythagorean neutrosophic sets with a new correlation measure that will consider all three degrees of membership: the truth-membership, indeterminacy-membership and falsity-membership degree and will satisfy the Pythagorean constraint. Complement, union and intersection are introduced on Pythagorean neutrosophic sets and a normalized correlation coefficient is introduced that is bounded, symmetric, and identity. The suggested correlation value is then used to correlate observed behavioural indicators to threat categories that have been pre-defined. A case study of a real threat identification scenario shows that the framework is applicable in practice through the use of behavioural characteristics like thermal signature, pattern of movement, weapon handling and communication activity. The values of correlation obtained give a good separation of the various behavioural profiles and are close to the correct classification of the most likely threat category for each target for uncertain information. A series of visualization and analytical methods such as heatmaps, normalized heatmaps, two-dimensional and three-dimensional bar graphs, surface plots, spline interpolation, principal component analysis (PCA), t-distributed stochastic neighbour embedding (t-SNE) and parallel coordinate plots are used to further validate the proposed methodology. The stability, interpretability and discriminatory power of the proposed correlation measure is confirmed by the graphical analysis. The proposed Pythagorean neutrosophic framework is an interpretable mathematical model that manages uncertainty-aware threat identification, and is a potential alternative to the classical similarity measures in the field of security intelligence, decision support systems and other applications using incomplete and conflicting information.