This paper defines the notion of cycle symmetry, which extends the traditional automorphism-based symmetry and enables application of symmetry reduction to a broader class of asymmetric systems. The study also shows that both cycle symmetry group and cycle symmetry generated group can be used to produce a quotient structure that is bisimilar to the original model. Furthermore, the extension of symmetry reduction over three-valued models is investigated. The quotient structure of a three-valued model is defined and induced by a permutation group and extends to both automorphism-based symmetry reduction and cycle symmetry reduction to three-valued models. Finally, the study analyzes the relationship between symmetry reduction of a three-valued model and classical models induced by it. Both approaches can lead to the same reduced quotient structure of the original model.