Technological advancements and artificial intelligence raise security concerns, with facial recognition being a particularly effective security measure. Choosing the best facial recognition software involves a comprehensive decision-making approach due to its sensitivity and potential ambiguities, ensuring the highest level of security. The main aim of the research is to introduce a new theoretical framework called the complex picture fuzzy soft set (CPFS-set), which manages information-based uncertainty, periodicity, and vagueness by combining the flexibility of soft sets and complex picture fuzzy sets. Basic concepts, such as types and set operations, are examined mathematically with numerical examples to clarify the ideas. An intelligent decision-support mechanism is developed using a robust algorithm to illustrate the construction and computation stages of facial recognition software evaluation with the CPFS-set. This comprehensive analysis helps stakeholders make informed decisions based on empirical data and rigorous evaluation.

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.

Typically, symptoms are considered when diagnosing specific illnesses, but this does not apply to liver disorder (LDR), as it encompasses a range of symptoms that are common to various other diseases. The most effective approach is to assess a patient’s susceptibility to LDR by utilizing the features of relevant laboratory tests as metrics. This study introduces the concepts of interval-valued complex fuzzy hypersoft set (IVCFHSS), a novel mathematical framework, to aggregate and characterize patients’ susceptibility to LDR. This model is capable of addressing the combined effects of the uncertain nature of the data, sub-parametric parameter values, and periodicity. Five laboratory tests associated with LDR, are considered as parameters, and the corresponding characteristics of such laboratory tests are taken as parametric values. An easily implementable multi-attribute decision-making (MADM) scenario is employed to evaluate a proposed method for assessing patients’ susceptibility to LDR using the IVCFHSS matrix aggregations. A structural comparison of the proposed model with several pertinent, contemporary models demonstrates its flexibility and reliability.

The Fermatean fuzzy soft set (FFSS) is a natural extension of the intuitionistic fuzzy soft set (IFSS) and the Pythagorean fuzzy soft set (PyFSS). It retains the corresponding benefits of IFSS, PyFSS, and their extensions, including the ability to represent an entity from both favorable and adverse perspectives. It renders it feasible to mimic real-world situations where uncertainty is prevalent more precisely. It is possible to portray uncertain circumstances more effectively with the incorporated dimension of hesitation degree. The current study presents an innovative form of FFSS, known as complex Fermatean fuzzy soft set (cFRFSS), aiming at addressing the complexities related to data uncertainty and periodicity. The basic idea of cFRFSS, including set-theoretic operations and properties, is demonstrated numerically, and associated results are provided. To mitigate inconsistent information, modified entropy metrics for cFRFSS are put forward in the following section. Then, to assist university managers in assessing the research output of their faculty members within the institution, a robust method employing suggested cFRFSS-based entropy measures is offered. The suggested strategy’s adaptability is assessed by contrasting it with other strategies that have been previously put forth.