In the paper, \w introduce the notion of an action Yx as a generalization of the notion of a module, and the notion of a norm D: Yx ®F, where F is a field and D(xg) 6 (g’) = 6 (g) 6 (xg') as well as the notion of fuzzy norm, where D:gx® [0, 1] ÍR, with R the set of all real numbers. A great many standards mappings Oil algebraic systems can be modeled On norms as shown in the examples and it is seen that Ker D= {gl D(g) = O} has many useful properties. Some are explored. In the discussion of the discussion of fuzzy forms as they relate to the complements of sub actions Nx of Yx .