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.

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 ($\mathcal{CFHS}$) 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 $\mathcal{CFHS}$ 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 $\mathcal{CFHS}$ set and $\mathcal{CFHS}$-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 $\mathcal{CFHS}$-mapping, which identifies the disease and selects the optimum medication correctly. Furthermore, a generalized $\mathcal{CFHS}$-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.

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 attribute-valued 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.

Solid waste management has gained a reputation among environmentalists as it poses a significant threat to the environment when done incorrectly and leading to effects longing for more than a century. Current solid waste management (SWM) concerns are inextricably linked to maintaining mandated organic waste treatment and reusing objectives following European directive regulations. Characterizing and spreading uncertainty, as well as verifying forecasts, are all challenges in decision-making. This study presents a multi-attribute decision-making approach based on entropy and similarity measures to evaluate SWM strategies. This research examined the novelty of the complex fuzzy HyperSoft set (CFHSS), which may respond to instabilities, ambiguity, and vagueness of facts in knowledge by simultaneously putting into consideration the amplitude and phase characteristics (P-terms) of complex numbers (C-numbers). The presented structure is the most suitable option for exploring SWM concerns as it allows for a more comprehensive array of membership values, and the periodic nature of the content can be expressed in P-terms to widen the content to a unit circle in a dynamic reference frame through the specification of the fuzzy HyperSoft set (FHSS). Secondly, the features in CFHSS may be further sub-divided into attribute values for easier comprehension. The paper also illustrates the apparent connection between CFHSS similarity measures (SM) and entropy (ENT) and explores colloquial meaning. These strategies may be used to determine the best approach from a group of possibilities that have a variety of applications in the field of optimization. The recommended methodology’s reliability and effectiveness are examined by evaluating the acquired findings to those of several prior studies. An assessment is done using various parameter values to validate the robustness of the suggested approach.

Infectious diseases are one of the leading causes of death all over the world. This study aims to define the debates around the diagnosis of infectious diseases and their associated issues. After looking at the side effects of Infectious Diseases, it becomes difficult to distinguish the types of Infectious Diseases and their severities. It is difficult to detect the efficiency in treating a patient record and predicting the length of medicine because the indeterminacy, false components, amplitude term (A-term), phase term (P-term), and sub parametric values are commonly rejected in terms of practical evaluation. This paper introduces the Complex Neutrosophic Hypersoft (CNHS) set and CNHS mapping with its inverse mapping to overcome these limitations. This theory will be more flexible in three ways. First, it includes indeterminacy and falsity components, which will utilise parametric values to analyse data in all three dimensions of the patient’s illness: positive, indeterminant, and negative. Secondly, for easier understanding, it separates the various attributes into distinct attribute-valued sets. Third, it provides for a large range of membership function values by expanding membership to the unit circle on an Argand plane and introducing an additional term known as the P-term to account for the periodic character of the data. To correctly analyse the problem, these principles can be coupled with scientific modelling. This study demonstrates a correlation between symptoms and treatments. A table with a fuzzily defined gap between 0 and 1 is created for different types of infectious diseases. The computation is based on CNHS mapping in order to properly detect the condition and select the appropriate prescription for each patient’s ailment. Eventually, a generalised CNHS mapping is offered, which can assist a doctor in releasing the chronology of the patient’s health status and predicting the time frame of therapy until the sickness is cleared.

The Pythagorean fuzzy set (PFS), which Yager extended, is a novel tool for dealing with ambiguity when considering membership(MS) grade p and non-membership (NMS) q that fulfil the criteria $p^{2} + q^{2} \leq 1$ allowing the structure to characterise fuzziness more thoroughly and precisely than intuitionistic fuzzy sets. The Pythagorean Fuzzy Hypersoft (PFHS) set theory is a useful method for dealing with abnormalities and uncomfortable information in real-life situations. The Pythagorean fuzzy set and the Hypersoft set, which comprise the truthfulness grade (TG) and falsehood grade (FG) in the Pythagorean environment, are combined in the PFHS principle. This study tries to define the arguments around allergy diagnosis and the effects that arise with it. After considering the dire outcomes of Allergies, it becomes challenging to distinguish between the various types of Allergies and their complexity. Because the false portions of practical assessments are usually ignored, precision in the person’s developmental history is difficult to recognize, and number of sessions cannot be projected. This work presents the PFHS set and PFHS mapping with its inverse mapping (INM) to alleviate these constraints. These notions are capable and necessary for correctly analyzing the problem by combining it with scientific modelling. This study establishes a link between symptoms and medications, lowering the narrative’s complexity. For the various types of allergies, a table based on a fuzzy interval between [0, 1] is created. The techniques that are based on PFHS-mapping, which is used to effectively identify a problem then choose the right treatment for each patient’s condition.