The Study of HIV Diagnosis Using Complex Fuzzy Hypersoft Mapping and Proposing Appropriate Treatment

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.