Open AccessFuzzy cosets in AG-groups
Author(s) -
Aman Ullah,
Muhammad Ibrahim,
Tareq Saeed
Publication year - 2022
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.