Fuzzy Cosets and Quotient Fuzzy AG-subgroups

Abstract

In this paper we extend the concept of fuzzy AG-subgroups. We introduce some results in normal fuzzy AG-subgroups. We define fuzzy cosets and quotient fuzzy AG-subgroups, and prove that the sets of their collection form an AG-subgroup and fuzzy AG-subgroup respectively. We also introduce the fuzzy Lagrange's Theorem of AG-subgroup. It is known that the condition $\mu(xy)=\mu(yx)$ holds for all $x,y$ in fuzzy subgroups if $\mu$ is normal, but in fuzzy AG-subgroup we show that it holds without normality.