In this paper, we have established some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we introduced the basic results of complex fuzzy sets with their examples such as complex fuzzy union, complex fuzzy intersection, complex fuzzy complement, complex fuzzy Cartesian product, complex fuzzy bounded sum, complex fuzzy bounded difference, complex fuzzy algebraic sum, and complex fuzzy algebraic product. We established a new algorithm for the application of a complex fuzzy set in denoising data. We employed CFSs in data denoising using Fast Fourier transform since the phase term of CFS is periodic and performs like a Fast Fourier transform. We introduced a novel methodology for exploiting a CFS to develop a new model of the matrix, in which we identified a reference signal and removed noise from a specific signal.