The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex fuzzy relation are introduced.