Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment

The picture fuzzy set was introduced by Coung. It is a generalization of the intuitionistic fuzzy set, giving the notion of neutral membership degrees along with the positive and negative ones. Lie groups and Lie algebras have become indispensable for a lot of fields in mathematical and intellectual...

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Autores principales: Kousar, Sajida, Arshad, Sidra, Kausar, Nasreen, Hong, Tzung-Pei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10027600/
http://dx.doi.org/10.1007/s44196-023-00213-w
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author Kousar, Sajida
Arshad, Sidra
Kausar, Nasreen
Hong, Tzung-Pei
author_facet Kousar, Sajida
Arshad, Sidra
Kausar, Nasreen
Hong, Tzung-Pei
author_sort Kousar, Sajida
collection PubMed
description The picture fuzzy set was introduced by Coung. It is a generalization of the intuitionistic fuzzy set, giving the notion of neutral membership degrees along with the positive and negative ones. Lie groups and Lie algebras have become indispensable for a lot of fields in mathematical and intellectual physics. In 1872, Lie began his work in the field of continuous transformation groups, later named after him as Lie groups. These have become a fundamental body of interest in themselves. In this paper, the authors presented the notion of the picture fuzzy Lie algebra, picture fuzzy Lie sub-algebra, ideal, and homomorphism. Derived and lower central series of picture fuzzy Lie ideals are constructed to define and analyse solvable and nilpotent picture fuzzy Lie ideals.
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spelling pubmed-100276002023-03-21 Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment Kousar, Sajida Arshad, Sidra Kausar, Nasreen Hong, Tzung-Pei Int J Comput Intell Syst Research Article The picture fuzzy set was introduced by Coung. It is a generalization of the intuitionistic fuzzy set, giving the notion of neutral membership degrees along with the positive and negative ones. Lie groups and Lie algebras have become indispensable for a lot of fields in mathematical and intellectual physics. In 1872, Lie began his work in the field of continuous transformation groups, later named after him as Lie groups. These have become a fundamental body of interest in themselves. In this paper, the authors presented the notion of the picture fuzzy Lie algebra, picture fuzzy Lie sub-algebra, ideal, and homomorphism. Derived and lower central series of picture fuzzy Lie ideals are constructed to define and analyse solvable and nilpotent picture fuzzy Lie ideals. Springer Netherlands 2023-03-21 2023 /pmc/articles/PMC10027600/ http://dx.doi.org/10.1007/s44196-023-00213-w Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research Article
Kousar, Sajida
Arshad, Sidra
Kausar, Nasreen
Hong, Tzung-Pei
Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title_full Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title_fullStr Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title_full_unstemmed Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title_short Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
title_sort construction of nilpotent and solvable lie algebra in picture fuzzy environment
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10027600/
http://dx.doi.org/10.1007/s44196-023-00213-w
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