Eigen Neutrosophic Z- Set and Neutrosophic Z- Relation

P. Sheeba Maybell; M.M. Shanmugapriya

Authors

P. Sheeba Maybell Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore, Tamil Nadu, India;
M.M. Shanmugapriya Dept. of Mathematics, Karpagam Academy of Higher Education, Coimbatore, Tamil Nadu, India;

Keywords:

Neutrosophic Z-set, Neutrosophic Z-relation, Neutrosophic Z-Matrices, Eigen Neutrosophic Z-set, Composition operators, Decision-making uncertainty modelling.

Abstract

This paper introduces an innovative framework for computing the Greatest Eigen
Neutrosophic Z-set and the Least Eigen Neutrosophic Z-set using the composition operators, namely
max-min-min and min-max-max. The proposed Eigen Neutrosophic Z-set, along with the
Neutrosophic Z-relation, remains constant across different computational perspectives. This study
addresses the limitation of existing neutrosophic and fuzzy models that fail to effectively capture
eigen-based relationships under uncertainty by introducing the Eigen Neutrosophic Z-set framework
for more consistent and interpretable decision analysis. Furthermore, Neutrosophic Z-matrices are
developed, and their properties are examined in relation to Neutrosophic Z-relations. In this paper
several similarity relations among Neutrosophic Z-matrices are presented, along with discussions on
their permutations and the invertibility characteristics. Two distinct algorithms are formulated to
establish the Greatest Eigen Neutrosophic Z-set and the Least Eigen Neutrosophic Z-set,
accompanied by a numerical example. Additionally, a practical application is provided to
demonstrate the enhancement of score value while addressing both effectiveness and uncertainty for
future advancements of hotel management decision-making systems.

DOI 10.5281/zenodo.17662233