Abstract
Hypersoft set (HSS) was proposed in 2018 as a generalization of the soft set (SS). In this paper, the novelty of complex multi-fuzzy hypersoft set (CMFHSS) is discussed, which can deal with uncertainties, vagueness, and unclearness of data that lie in the information by taking into account the amplitude and phase terms (P-terms) of the complex numbers (C-numbers) at the same time. This CMFHSS establishes a hybrid framework of the multi-fuzzy set (MFS) and HSS characterized in a complex system. This framework is more flexible in two ways; firstly, it permits a wide range of values for membership function by expanding them to the unit circle in a complex frame of reference through characterization of the multi-fuzzy hypersoft set (MFHSS) involves an additional term called the P-terms to consider the periodic nature of the information. Secondly, in CMFHSS, the attributes can be further sub-partitioned into attribute values for a better understanding. We characterize its fundamental operations as a complement, union, and intersection and support them with examples. We develop the proverbial meaning of similarity measures (SM) and entropy (ENT) of CMFHSS and present the fundamental relationship. These tools can be utilized to figure out the best alternative out of a bunch that has various applications in the field of optimization. Additionally, mathematical models are given to analyze the reliability and predominance of the established methodologies. Moreover, the advantages and comparative analysis of the proposed measures with existing measures are also depicted in detail. Lastly, the mathematical models are given to represent the validity and applicability of the presented measures.