Karyati
The Green relations on semigroups have been introduced by Howie. They are right Green relation R, left Green relation L and (two sided) Green relation I. The right Green relation R is defined as ((x, y)∈S×S|(y)R) with (x)R denotes the right ideal generated by an element x (or called the principle right ideal generated by x. The definition of the left Green relation L and the Green relation I are similar to the definition of the right Green relation. In this study, we will construct the definition of the fuzzy right Green relation (denoted by RF), the fuzzy left Green relation (denoted by LF) and the fuzzy Green relation (denoted by IF) on a semigroup. First we define a fuzzy ideal (right/left) generated by a fuzzy subset (a fuzzy principle ideal) on a semigroup and their examples. Based on, the fuzzy principle ideal definition, we define a fuzzy (right/left) Green relation on a semigroup. The fuzzy subset μ and ρ are fuzzy (right/left) Green related if and only if the fuzzy (right/left) ideal generated by μ is equal to the fuzzy (right/left) ideal generated by ρ. © Medwell Journals, 2017.
Department of Mathematics Education, Yogyakarta State University, Yogyakarta, Indonesia
