Fuzzy cosets in AG-groups | Zendy

Aman Ullah | Zendy; Muhammad Ibrahim | Zendy; Tareq Saeed | Zendy

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Fuzzy cosets in AG-groups

Author(s) -

Aman Ullah,

Muhammad Ibrahim,

Tareq Saeed

Publication year - 2021

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022185

Subject(s) - coset , mathematics , quotient , fuzzy logic , homomorphism , group (periodic table) , normal subgroup , order (exchange) , quotient group , discrete mathematics , combinatorics , algebra over a field , torsion subgroup , pure mathematics , cyclic group , physics , computer science , artificial intelligence , quantum mechanics , abelian group , finance , economics , elementary abelian group

In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if $ A $ is any fuzzy AG-subgroup of $ G $, then $ \mu_{A}(xy) = \mu_{A}(yx) $ for all $ x, \, y\in G $, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number $ [G:A] $. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange's theorem of finite AG-group is also introduced.

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