In recent times, the practice of involving the concept of fuzzy in graph theory has led to various helpful findings. More precisely, large numbers of real-life problems have been modelled into graph with the involvement of fuzzy concepts. In this paper, some planar graphs like Wheel Graph, Ladder Graph, And Circular Graph are studied with the idea of Fuzzy Anti-Magic Graphs. Moreover, total coloring and an algorithm is discussed to build an Intuitionistic Fuzzy Face Anti-Magic Planar Graph.