Quaternionic Fuzzy Sets

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization traditional and complex based on quaternions. The novelty that the range membership function set quaternions with modulus less than or equal to one, which real imaginary parts can be used for four different features. discussion made intuitive interpretation quaternion-valued grades possible applications QFSs. Several operations, including complement, union, intersection, aggregation QFSs, presented. Quaternionic relations their composition also investigated. QFS designed maintain advantages FS CFS, while benefiting from properties Cuts rotational invariance operations demonstrate particularity membership.