(untitled) (Faculty of Education Scientific Journal, 2024)
The free product of fuzzy sets in a group theory is such attractive topic for many researchers. This product, which lies between the sup-min and sup-max products, has number of important properties and also some potential applications. It is also demonstrated that, the standard results for the product of two subgroups in a group are simulated by the free product. The employing of previous concepts and results within the fuzzy set framework is made possible by its relationship to group theory. Here, in this paper, we shall study the free product of two fuzzy sets in a groupoid in order to obtain some results regarding to the subject of the free product.