Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem
In this study, we introduce two novel matrix concepts in the neutrosophic fuzzy domain: range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and kernelsymmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices. These matrices are defined analogously to EP-matr...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-04-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/15AlgebraicProperties.pdf |
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| author | P.Tharini C. Devi Shyamala Mary P.Tharaniya S. Prathap S. Ramkumar G. Dhanavel |
| author_facet | P.Tharini C. Devi Shyamala Mary P.Tharaniya S. Prathap S. Ramkumar G. Dhanavel |
| author_sort | P.Tharini |
| collection | DOAJ |
| description | In this study, we introduce two novel matrix concepts in the neutrosophic fuzzy domain: range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and kernelsymmetric 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 rangesymmetric 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- kernel-symmetric in Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, the converse does not necessarily hold. We further discuss the connections between kernel-symmetric, k- kernelsymmetric 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. |
| format | Article |
| id | doaj-art-92df0724d102479280df4fc16db18f46 |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-92df0724d102479280df4fc16db18f462025-08-25T10:15:44ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-04-018024727710.5281/zenodo.14707588Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making ProblemP.ThariniC. Devi Shyamala MaryP.TharaniyaS. PrathapS. RamkumarG. DhanavelIn this study, we introduce two novel matrix concepts in the neutrosophic fuzzy domain: range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and kernelsymmetric 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 rangesymmetric 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- kernel-symmetric in Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, the converse does not necessarily hold. We further discuss the connections between kernel-symmetric, k- kernelsymmetric 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. https://fs.unm.edu/NSS/15AlgebraicProperties.pdfinterval-valued quadri partitioned neutrosophic fuzzy matricesrange-symmetric interval-valued quadri partitioned neutrosophic fuzzy matriceskernel-symmetric interval-valued quadri partitioned neutrosophic fuzzy matricesmoore-penrose inversedecision-making |
| spellingShingle | P.Tharini C. Devi Shyamala Mary P.Tharaniya S. Prathap S. Ramkumar 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 interval-valued quadri partitioned neutrosophic fuzzy matrices range-symmetric interval-valued quadri partitioned neutrosophic fuzzy matrices kernel-symmetric interval-valued quadri partitioned neutrosophic fuzzy matrices moore-penrose inverse decision-making |
| title | Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem |
| title_full | Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem |
| title_fullStr | Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem |
| title_full_unstemmed | Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem |
| title_short | Algebraic Properties of Interval -Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and their Application in Multi-Criteria Decision- Making Problem |
| title_sort | algebraic properties of interval valued quadri partitioned neutrosophic fuzzy matrices and their application in multi criteria decision making problem |
| topic | interval-valued quadri partitioned neutrosophic fuzzy matrices range-symmetric interval-valued quadri partitioned neutrosophic fuzzy matrices kernel-symmetric interval-valued quadri partitioned neutrosophic fuzzy matrices moore-penrose inverse decision-making |
| url | https://fs.unm.edu/NSS/15AlgebraicProperties.pdf |
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