Article ID: MTJPAM-D-24-00143

Title: On multi q-Rung orthopair fuzzy Lie algebraic structures


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00143; Volume 7 / Issue 3 / Year 2025, Pages 144-162

Document Type: Research Paper

Author(s): ‪Bishnupada Debnath a

aDepartment of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh (791112), Itanagar, Arunachal Pradesh, India

Received: 7 September 2024, Accepted: 3 March 2026, Published: 14 November 2026

Corresponding Author: Bishnupada Debnath (Email address: drbishnumathlab2020@gmail.com)

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Abstract

In neutrosophic settings the membership, indeterminacy and non-membership degrees are determined by a single expert whereas in multi q-Rung orthopair fuzzy settings the same components are evaluated by hiring a group of independent expert which is more efficient, reliant and consistent than neutrosophic logic which motivates us to introduce for the first time the concept of Lie subalgebra and Lie ideal in the light of the concept of Smarandache’s multi q-Rung orthopair fuzzy settings as a generalization of neutrosophic Lie subalgebra and Lie ideals. In this study, we proved that the intersection (resp. Cartesian product) of two multi q-Rung orthopair fuzzy Lie subalgebras is multi q-Rung orthopair fuzzy Lie subalgebra. Some more fundamental results and properties are also derived. In the light of analytical method we proved that every multi q-Rung orthopair fuzzy Lie ideal is multi q-Rung orthopair fuzzy Lie subalgebra but not reversible which is shown by utilizing counter example.

We also derive some preservation aspects of multi q-Rung orthopair fuzzy Lie subalgebra and Lie ideal, solvable and nilpotent multi q-Rung orthopair fuzzy Lie ideals under Lie homomorphism and its inverse. A significant finding from this study is homomorphic image of solvable (resp. nilpotent) multi q-Rung orthopair fuzzy Lie ideals is solvable (resp. nilpotent) multi q-Rung orthopair fuzzy Lie ideals. Finally, with the help of these newly defined concepts some more interesting results on solvable and nilpotent multi q-Rung orthopair fuzzy Lie ideals are investigated as a part of application. The findings offered here add to the larger framework of Lie algebraic theory, offering fresh perspectives for further study of the structural characteristics of BCK and BCI algebra using multi q-Rung orthopair fuzzy sets.

Keywords: Lie algebra, Lie ideal, MqROF set, MqROF Lie subalgebra, MqROF Lie ideal, solvable MqROF Lie ideal, nilpotent MqROF Lie ideal

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Cite this article

How to cite this article: ‪B. Debnath, On multi q-Rung orthopair fuzzy Lie algebraic structures, Montes Taurus J. Pure Appl. Math. 7 (3), 144-162, 2025; Article ID: MTJPAM-D-24-00143.