Affiliations: School of Mathematical Sciences, University of Science and Technology of China, Hefei, China | Department of Mathematics, Abdul Wali Khan University, Mardan, K. P. K., Pakistan | Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
Note: [] Corresponding author. F. Yousafzai, School of Mathematical Sciences, University of Science and Technology of China, Hefei, China. E-mail: yousafzaimath@yahoo.com
Abstract: We have introduced and characterized a fully regular (V-regular) class of an ordered $\mathcal{AG}$-groupoid in terms of fuzzy (left, right, two-sided, interior, bi-, generalized bi- and quasi) ideals. We have shown that all these fuzzy ideals need not to be coincide in an ordered $\mathcal{AG}$-groupoid $\mathcal{S}$ even if $\mathcal{S}$ has a left identity but on the other hand, it has been shown that all these fuzzy ideals coincide in a V-regular ordered $\mathcal{AG}$-groupoid with a left identity.
