@article{Ullah2022, 
author = {Aman Ullah and Muhammad Ibrahim and Tareq Saeed},
title = {Fuzzy cosets in AG-groups},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {3321-3344},
keywords = {AG-group, fuzzy AG-subgroup, fuzzy normal AG-subgroup, fuzzy coset and fuzzy quotient AG-subgroups},
url = {https://www.sciopen.com/article/10.3934/math.2022185},
doi = {10.3934/math.2022185},
abstract = {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        μ          A        (  x  y  )  =      μ          A        (  y  x  ) for all    x  ,    y  ∈  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.}
}