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COVID-19 has shaken the entire world economy and affected millions of people in a brief period. COVID-19 has numerous overlapping symptoms with other upper respiratory conditions, making it hard for diagnosticians to diagnose correctly. Several mathematical models have been presented for its diagnosis and treatment. This article delivers a mathematical framework based on a novel agile fuzzy-like arrangement, namely, the complex fuzzy hypersoft (CFHS) set, which is a formation of the complex fuzzy (CF) set and the hypersoft set (an extension of soft set). First, the elementary theory of CFHS is developed, which considers the amplitude term (A-term) and the phase term (P-term) of the complex numbers simultaneously to tackle uncertainty, ambivalence, and mediocrity of data. In two components, this new fuzzy-like hybrid theory is versatile. First, it provides access to a broad spectrum of membership function values by broadening them to the unit circle on an Argand plane and incorporating an additional term, the P-term, to accommodate the data’s periodic nature. Second, it categorizes the distinct attribute into corresponding sub-valued sets for better understanding. The CFHS set and CFHS-mapping with its inverse mapping (INM) can manage such issues. Our proposed framework is validated by a study establishing a link between COVID-19 symptoms and medicines. For the COVID-19 types, a table is constructed relying on the fuzzy interval of [0,1]. The computation is based on CFHS-mapping, which identifies the disease and selects the optimum medication correctly. Furthermore, a generalized CFHS-mapping is provided, which can help a specialist extract the patient’s health record and predict how long it will take to overcome the infection.

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.

HIV is still a global epidemic more than 40 years after it was described initially, impacting mainly Sub-Saharan Africa, Southeast Asia, and Latin America. HIV is an RNA retrovirus that wreaks havoc on the immune system, making the infected individual vulnerable to opportunistic pathologies. For the diagnosis and therapy of infected patients, several models have been proposed in literature. The main goal of this paper is to present an innovative mathematical model for diagnosing and treating this pandemic based on a unique flexible fuzzy-like structure called the Complex Fuzzy Hypersoft (CFHS) set, which is a glued structure of complex fuzzy (CF) set and hypersoft sets (an extension of soft set). To address ambiguity and unclear data, the basic theory of CFHS set is created, which examines the amplitude term (A-term) and phase term (P-term) of complex numbers concurrently. In two aspects, this new fuzzy-like hybrid theory is adaptable. First, extending membership function values to the unit circle on an Argand plane and including an extra term, the P-term, to suit the recurring character of data that provide access to a wide range of membership function values. Second, it categorises the different attributes into matching disjoint attributevalued sets for a more straightforward interpretation; it's tough to identify which HIV is and how serious it is after looking at the HIV side effects. To deal with such problems, the CFHS set, and CFHS-mapping with its inverse mapping is utilised. These concepts are practical and required for adequately assessing the situation using mathematical modelling. This investigation shows a relationship between symptoms and medications, making the story easier to follow. A table is constructed for the HIV kinds based on a fuzzy interval of [0, 1]. The calculation is based on CFHS-mapping, which correctly diagnoses the condition and prescribes the best medicine. A generalised CFHS-mapping is also offered, which can assist a specialist in extracting the patient's improvement record and estimating how long it will take to eradicate the infection.

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