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.

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.