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.

Intuitionistic fuzzy hypersoft set is an extension of the intuitionistic fuzzy soft set used to express insufficient evaluation, uncertainty, and anxiety in decision-making. It is a new technique to realize computational intelligence and decision-making under uncertain conditions. The intuitionistic fuzzy hypersoft set can deal with uncertain and fuzzy information more effectively. The concepts and properties of the correlation coefficient and the weighted correlation coefficient of the intuitionistic fuzzy hypersoft sets are proposed in the following research. A prioritization technique for order preference by similarity to ideal solution (TOPSIS) based on correlation coefficients and weighted correlation coefficients is introduced under the intuitionistic fuzzy hypersoft sets. We also introduced aggregation operators, such as intuitionistic fuzzy hypersoft weighted average and intuitionistic fuzzy hypersoft weighted geometric operators. Based on the established TOPSIS method and aggregation operators, the decision-making algorithm is proposed under an intuitionistic fuzzy hypersoft environment to resolve uncertain and confusing information. A case study on decision-making difficulties proves the application of the proposed algorithm. Finally, a comparative analysis with the advantages, effectiveness, flexibility, and numerous existing studies demonstrates this method's effectiveness.

Cosine and cotangent similarity measurements are critical in applications for determining degrees of difference and similarity between objects. In the literature, numerous similarity measures for various extensions of fuzzy set, soft set, Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFSs) and HyperSoft Sets (HSSs) have been explored. Neutrosophic HyperSoft Sets (NHSSs), on the other hand, has fewer cosine and cotangent similarity measures. In this paper, we propose the trigonometric similarity measures of NHSSs. We further investigate the basic operators, theorems, and propositions for the proposed similarity measures. We know that global warming causes environmental problems. One of applications for solving global warming is the concept of renewable energy. To show the effectiveness of the proposed similarity measures, we apply them to renewable energy source selection problems. The study reveals the best geographical area to install the energy production units, under some technical attributive factors. To check the validity and superiority of the proposed work, it is compared with some existing techniques which reveal that, decision-making problems with further bifurcated attributes, have more accurate and precise results and can only be solved with this technique. In the future, the proposed techniques can be applied to case studies, in which attributes are more than one and further bifurcated along with more than one decision-maker. Also, this proposed work can be extended for several existing hybrids of hypersoft sets, intuitionistic hypersoft, neutrosophic hypersoft set, bi-polar hypersoft, m-polar hypersoft sets, and Pythagorean hypersoft set to solve Multi-Criteria Decision Making (MCDM) problems.

Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.

Hepatitis is regarded as one of the leading causes of death around the globe. This paper aims to characterize the discussions related to the diagnosis of Hepatitis with their related problems. After examining the side effects of Hepatitis, it encases similar indications, and it is hard to distinguish the precise type of Hepatitis with its seriousness. Since in practical assessment, the indeterminacy and falsity parts are frequently dismissed, and because of this issue, it’s hard to notice the precision in the patient’s progress history and can’t foresee the period of treatment. The Neutrosophic Hypersoft (NHS) set and NHS mapping with its inverse mapping to eliminate these limits are presented in this paper. These ideas are capable and essential to analyze the issue properly by interfacing it with scientific modeling. This investigation builds up a connection between symptoms and medicines, which diminishes the difficulty of the narrative. A table depending on a fuzzy interval between [0, 1] for the sorts of Hepatitis is constructed. The calculation depends on NHS mapping to adequately recognize the disease and choose the best medication for each patient’s relating sickness. Finally, the generalized NHS mapping is presented, which will encourage a specialist to extricate the patient’s progress history and to foresee the time of treatment till the infection is relieved.