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

D.Vidhya; S.Jafari; G. Nordo

Authors

D.Vidhya Department of Science and Humanities, Karpagam Institute of Technology, Coimbatore-641105, Tamilnadu, India;
S.Jafari Professor of Mathematics, College of Vestsjaelland South Herrestarede 11, Slagelse, Denmark;
G. Nordo MIFT Department of Mathematical and Computer Science, Physical Sciences and Earth Sciences - University of Messina, 98166 Sant’ Agata, Messina, Italy;

Keywords:

Principal Component Analysis (PCA), Neutrosophic Logic, Dimensionality Reductio

Abstract

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.

DOI 10.5281/zenodo.17312950