Generalized Inverse of Quadri-Partitioned Neutrosophic  Fuzzy Matrices and its Application to Decision-Making  Problems

R. Jaya; S. Vimala

Authors

R. Jaya Research scholar, Department of Mathematics, Mother Teresa Women's University, Kodaikanal, Tamilnadu, India.
S. Vimala Department of Mathematics, Mother Teresa Women's University, Kodaikanal, Tamilnadu, India.

Keywords:

Quadri-Partitioned Neutrosophic Fuzzy sets, Quadri-Partitioned Neutrosophic Fuzzy Matrices, generalized inverse (g-inverse), Moore-Penrose inverse, minus ordering.

Abstract

This paper presents a novel framework for computing the generalized inverse (g-inverse)
and the Moore-Penrose inverse of Quadri-Partitioned Neutrosophic Fuzzy Matrices (QPNFMs). To
the best of our knowledge, no existing algorithm addresses the computation of the g-inverse for
QPNFMs. In this study, we establish necessary and sufficient conditions for the existence of the
g-inverse and develop an efficient algorithm for its computation. Furthermore, we explore several
fundamental properties and theoretical results related to the g-inverse of QPNFMs, including
uniqueness conditions and algebraic structures. In addition to theoretical advancements, we
introduce a novel decision-making algorithm leveraging QPNFMs and their g-inverse. This
algorithm enhances decision analysis in complex and uncertain environments by effectively
handling indeterminate and inconsistent information. An illustrative example is provided to
demonstrate the practical applicability and computational efficiency of the proposed approach. The
results validate the accuracy of the g-inverse computation and highlight the utility of QPNFMs in
decision-making scenarios. Our findings offer a significant contribution to both matrix theory and
neutrosophic logic-based decision analysis, opening new avenues for future research in uncertainty
modeling and computational intelligence.

DOI: 10.5281/zenodo.15698304