  In this paper, we first study the arithmetic properties of intuitionistic
fuzzy number, the monotonicity of intuitionistic fuzzy function and the
derivative of intuitionistic fuzzy functions and then we study the fundamental
properties on monotone function. After that, we proposed a mean value theorem
for differentiable function in intuitionistic fuzzy calculus, from which we
derived a general version using Cauchy mean value theorem for intuitionistic
fuzzy calculus. At last, we give some examples and we also show as a corollary
that the mean value theorem is a special case of the Cauchy version of mean
value theorem.
