Abstract: 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 R^F), the fuzzy left Green relation (denoted by L^F) and the fuzzy Green relation (denoted by I^F) 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.