Novel distance measures based on complex fuzzy sets with applications in signals

In this paper, we discuss the further development of the theory of complex fuzzy sets (CFSs). The motivation for this extension is the utility of complex-valued function in membership grade which can express the two-dimensional ambiguous information that is prevalent in time-periodic phenomena. We introduce partial order relation on complex fuzzy sets. This partial order relation is then used to define the complex fuzzy maximal, minimal, maximum, and minimum elements. We propose new distance measures such as complex fuzzy distance measures and a complex fuzzy weighted distance measure. We establish some particular examples and basic results of the partial order relations and distance measures. Moreover, we utilize the complex fuzzy sets in signals and systems, because it is the specific form of the Fourier transform by restricting the range of Fourier transform to a complex unit disc. We establish a new algorithm based on the complex fuzzy distance measures and complex fuzzy weighted distance measures for applications in signals and systems by which we determine the degree of high resemblance of signals to the known signal. Further, the comparative study of the proposed distance measures with the Zhang distance measure, Hamming distance measure, and Normalized Hamming distance measure is discussed.