After defining the Mobius function on a partially ordered set, we describe briefly this function for the lattice of subsets of a finite set. Then we state the Mobius inversion formula carefully for subsets of a finite set. We use it to derive a set-theoretic principle of inclusion and exclusion for fuzzy subsets of a finite set X with n elements for a positive integer n. The counting technique is employed at the level sets of fuzzy subsets. The resultant summation is expressed in terms of various equivalent ways. A simple example is discussed illustrating the counting technique.

finite fuzzy set, Mobius function, inclusion-exclusion, set enumeration.