an extension of commutativity degree of finite groups

Let g be a finite group. the commutativity degree of g, written d(g), is defined as the ratio|{(x, y)|x, y in g, xy = yx}|/|g|^2. in this paper, we first extend this concept of finite groups to thecommutativity degree of fuzzy subgroups. then, by using the numerical solutions of the equation xy − zu eqiv t(mod n), we give explicit formulas for the commutativity degree of fuzzy subgroups of 2-generated groups of nilpotency class 2. finally we show that this method also works for a large class of finite groups, includingmetabelian groups.