DESCRIBING GREEN’S RELATIONS IN ORDERED Γ-GROUPOIDS USING A NEW CONCEPT: FUZZY SUBSETS - Iampan, Aiyared; Siripitukdet, Manoj (Italian Journal of Pure and Applied Mathematics, 2013)
This work extends the idea of the Green's relations \(R\), \(L\), \(I\) and the usual relation \(N\) of ordered groupoids to ordered Γ-groupoids in terms of fuzzy subsets, the concept of the Green's relations \(R\), \(L\), \(I\) and the usual relation \(N\) of ordered Γ-groupoids is introduced and investigated, which is an interesting for ordered Γ-groupoids and some interesting characterizations of the Green's relations \(R\), \(L\), \(I\) and the usual relation \(N\) of ordered Γ-groupoids are obtained. Also, we define relations \(R\)F, \(L\)F, \(I\)F and \(N\)F of ordered Γ-groupoids in terms of fuzzy subsets and we prove that \(R\)F = \(R\), \(L\)F = \(L\), \(I\)F = \(I\) and \(N\)F = \(N\) in the same way as of the results of Kehayopulu and Tsingelis [8].