By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the definition different from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two definitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomorphisms, and we obtain fuzzy analogues of many results concerning ordinary increasing functions and isomorphisms.