Advancing mathematical frontiers: A comprehensive study of the foundations of fermatean fuzzy soft linear spaces and its applications in supply chain management

This research introduces the concept of Fermatean Fuzzy Soft Linear Space (FFSLS) and conducts an in-depth investigation into its various properties and structural characteristics, along with illustration examples. These findings are significant because of their potential for real-life applications across diverse fields like decision-making, supply chain management, etc. Specifically, we define and elucidate the Cartesian product of Fermatean Fuzzy Soft Linear Spaces, Fermatean Fuzzy Soft Subspaces, Fermatean Fuzzy Soft Vectors, and Fermatean Fuzzy Soft Scalars through practical examples. Furthermore, we establish fundamental theorems relating to FFSLS, which contribute to the theoretical framework and practical utility of this novel mathematical construct. Understanding FFSLS and its associated components has improved theoretical comprehension and created more opportunities for real-world applications in a variety of practical situations, ranging from decision-making to engineering. We also built a machine learning based algorithms that used for better indicator performance. Therefore, this research serves as a fundamental contribution to the field of FFSLS, offering practical solutions to real-world problems. We also provide a real-life example at the end of the study that simplifies the decision process in a very easy and quick way.