Fuzzy roughness in Lie algebra by reference point

Eghdami, Hossien; Estaji, Ali Akbar; Haghdadi, Toktam

doi:10.3233/jifs-171620

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“…He then established a relation between this representation and nilpotent fuzzy Lie ideals. Eghdami et al [ 16 ] studied fuzzy roughness in Lie algebras and put forward the concept of reference points. Zadeh and Ameri [ 17 ], developed the notion of characterizing fuzzy subgroups as fuzzy Lie rings.…”

Section: Introductionmentioning

confidence: 99%

Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment

Kousar

Arshad

Kausar

et al. 2023

Int J Comput Intell Syst

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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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Section: Introductionmentioning

confidence: 99%