Integrating Neutrosophic Logic into Principal Component Analysis: A Python-Based Framework

Principal Component Analysis (PCA) is a widely used dimensionality reduction technique that transforms correlated variables into a smaller set of uncorrelated principal components. However, classical PCA assumes precise and crisp data, which may not hold true in real-world scenarios characterized by uncertainty and indeterminacy. To address this limitation, this study integrates Neutrosophic Logic into PCA, forming a robust framework capable of handling truth (T), indeterminacy (I), and falsity (F) values. The proposed methodology first converts neutrosophic data into crisp representations using an aggregation function, then applies PCA to extract principal components. A comparative analysis between normal PCA and Neutrosophic PCA is conducted using Python, highlighting how uncertainty impacts variance capture and eigenvector orientation. Visualization tools such as eigenvector plots, projection lines, and scree plots are employed to illustrate the findings. Results demonstrate that Neutrosophic PCA provides a more reliable representation of uncertain datasets without significant loss of variance information. This framework can be applied in fields such as pattern recognition, machine learning, and data-driven decision-making where uncertainty is inherent.