Omicron, so-called COVID-2, is an emerging variant of COVID-19 which is proved to be the most fatal amongst the other variants such as alpha, beta and gamma variants ($\alpha$, $\beta$, $\gamma$ variants) due to its stern and perilous nature. It has caused hazardous effects globally in a very short span of time. The diagnosis and medication of Omicron patients are both challenging undertakings for researchers (medical experts) due to the involvement of various uncertainties and the vagueness of its altering behavior. In this study, an algebraic approach, interval-valued fuzzy hypersoft set (iv-FHSS), is employed to assess the conditions of patients after the application of suitable medication. Firstly, the distance measures between two iv-FHSSs are formulated with a brief description some of its properties, then a multi-attribute decision-making framework is designed through the proposal of an algorithm. This framework consists of three phases of medication. In the first phase, the Omicron-diagnosed patients are shortlisted and an iv-FHSS is constructed for such patients and then they are medicated. Another iv-FHSS is constructed after their first medication. Similarly, the relevant iv-FHSSs are constructed after second and third medications in other phases. The distance measures of these post-medication-based iv-FHSSs are computed with pre-medication-based iv-FHSS and the monotone pattern of distance measures are analyzed. It is observed that a decreasing pattern of computed distance measures assures that the medication is working well and the patients are recovering. In case of an increasing pattern, the medication is changed and the same procedure is repeated for the assessment of its effects. This approach is reliable due to the consideration of parameters (symptoms) and sub parameters (sub symptoms) jointly as multi-argument approximations.

Soft set theory is considered as one of the best effective tool which provides parameterization approach to tackle the inadequacy of fuzzy set. So far, it has been applied to different mathematical concepts such as set operations, algebraic structure (e.g., group and ring theory) and topological spaces. Many researchers have studied classical concept of convex and concave set under fuzzy-like, soft-like and fuzzy soft-like environments. In this paper, new notions of (m, n)-convex and (m, n)- concave fuzzy soft sets are developed first and then their versions for first and second senses are established. Further some known classical results and properties are generalized under fuzzy soft set environment. Moreover, special cases of (m, n)-convexity on fuzzy soft sets are established

Interval-valued fuzzy hypersoft set ($ \mathbb{IVFHSS} $) is considered a pertinent fuzzy set-like model that is the combination of an interval-valued fuzzy set and a hypersoft set. It is more flexible and trustworthy for dealing with information-based uncertainties due to the consideration of interval-based hypersoft settings. This kind of setting enables the decision makers to approximate the alternatives in terms of interval-type opinions by considering multiple arguments concurrently. These features make it a fitting model for dealing with uncertain decision-making scenarios like the recruitment process. The vagueness arises in the recruitment process when the data obtained is hesitant. The analogous educational norms among the candidates may increase its complexity. Evaluation techniques focus on leveling hypersoft sets for grading several alternatives based on multi-arguments. When several alternatives have an identical status, such grading systems frequently encounter problems, making it challenging for decision-makers to select the preeminent alternative. This settlement of such an issue is the basis of this article. Thus, in this study, first the axiomatic notions of similarity measures between $ \mathbb{IVFHSS}s $ are characterized, and then their relevant theorem is proved. In order to provide a consistent decision-support framework for the recruitment process, a robust algorithm is proposed. Finally, the effectiveness, feasibility, and efficiency of the proposed model are demonstrated through the depiction of recruitment-based pattern recognition.

Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.