Neutrosophic Sets and Systems
Abstract
– In this study, we introduce two novel matrix concepts in the neutrosophic fuzzy domain: range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and kernel symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices. These matrices are defined analogously to EP-matrices within the complex domain. Initially, we establish fundamental characterizations of range-symmetric matrices and then derive the necessary and sufficient conditions under which an Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices becomes kernel-symmetric . A detailed analysis follows to explore the relationship between range symmetric and kernel-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices. Additionally, we introduce the concepts of Kernel and k-Kernel Symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, providing illustrative examples to demonstrate their application. Basic results for kernel-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices are derived, highlighting that while k-symmetric implies k- kerne-symmetric in Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, the converse does not necessarily hold. We further discuss the connections between kernel-symmetric, k- kernel symmetric and the Moore-Penrose inverse of Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, supported by numerical examples. The study culminates in an algorithm tailored for solving multi-criteria decision-making problems using Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, validated through an illustrative example that demonstrates its practical utility.
Recommended Citation
Tharini, P.; C. Devi Shyamala Mary; P. Tharaniya; S. Prathap; S. Ramkumar; and G. Dhanavel. "Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem." Neutrosophic Sets and Systems 80, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol80/iss1/15
