Riemannian Complex Fuzzy Sets with Applications in Signals

Abstract The objective of this paper is to introduce the innovative concept of Riemannian complex fuzzy sets (RCFSs). We discussed some new operations and laws of a RCFS such as Riemannian complex fuzzy union, intersection, complement, disjunctive sum, simple difference, bounded difference, simple product, Cartesian product, probabilistic sum, bold sum, convex linear sum, relations, and distance functions. We studied the basic results and particular examples of these operations. We used RCFSs in signals and systems because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using RCFSs for applications in signals and systems by which we identify a reference signal out of large input signals detected by a system. We restricted the amplitude of the inverse discrete Fourier transform for incoming signals and a reference signal. Thus, a method for measuring the resembling values of two signals is provided by which we can identify the reference signal.