Abstract: Principle of inclusion-exclusion on a weighted finite is studied by using combinatorial analysis method.Some new theorems for weighted principle of inclusion-exclusion are given and unify those of the previous studies.By using the new principle of inclusion-exclusion,enumerations for circular alternating permutation under identical transformation group and cycle group and dihedral group actions are studied.Some explicit enumerating formulas and combinatorial identities are obtained under identical transformation group and cycle group and dihedral group actions on circular alternating permutation.These results extend those of existing ones in some literatures.