Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment

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Kousar S., Arshad S., KAUSAR N., Hong T.

International Journal of Computational Intelligence Systems, vol.16, no.1, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s44196-023-00213-w
  • Journal Name: International Journal of Computational Intelligence Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, Directory of Open Access Journals
  • Keywords: Picture fuzzy set, Lie algebra, Picture fuzzy Lie algebra, Nilpotent and solvable picture fuzzy Lie algebra
  • Yıldız Technical University Affiliated: Yes


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.