Optimizing University Teaching Methods Using Algebraic Techniques in a Complex Fermatean Environment - Gang Wang; Zhen Wang (Decision Making: Applications in Management and Engineering, 2024)
In a university classroom, students exhibit varying levels of engagement, posing challenges for professors in delivering instruction effectively. While some students are highly engaged, others may struggle to keep pace, creating a demanding environment for the professor to manage while ensuring comprehensive learning. Consequently, the professor faces two primary options: either disregarding students with differing engagement levels or adopting an alternative teaching approach. An effective professor adapts their teaching methodology according to student engagement; however, determining the most suitable approach for the majority of students within a class is a complex task. The selection of an appropriate teaching mode is further complicated by various uncertain factors. This study seeks to develop a structured approach for selecting classroom teaching modes based on diverse levels of student engagement while considering multiple influencing factors. To achieve this, a novel model is introduced, namely the complex interval-valued Fermatean fuzzy set (CIVFFS), which integrates the characteristics of the complex Fermatean fuzzy set (CFFS) and the interval-valued Fermatean fuzzy set (IVFFS). The CIVFFS plays a crucial role in addressing the uncertain and incomplete information associated with various factors affecting classroom teaching methods. Four methods are proposed based on algebraic t-norms and t-conorms, namely the complex interval-valued Fermatean fuzzy weighted averaging (CIVFFWA) operator, the complex interval-valued Fermatean fuzzy ordered weighted averaging (CIVFFOWA) operator, the complex interval-valued Fermatean fuzzy weighted geometric (CIVFFWG) operator, and the complex interval-valued Fermatean fuzzy ordered weighted geometric (CIVFFOWG) operator, along with their respective properties. The proposed approach enables an evaluation of its effectiveness across different scenarios. An illustrative example is provided to demonstrate the practicality and reliability of the model and methods, highlighting their applicability in real-world contexts.