Abstract
Fermatean fuzzy \(\ddot{Z}\) numbers introduce a new decision-making framework which demonstrates greater capacity to handle uncertainty than traditional fuzzy set theory. The research study introduces a set of operational laws together with neutral aggregation operators which function as tools for handling Fermatean fuzzy \(\ddot{Z}\) numbers. The operators function as essential tools for multi-criteria decision-making because they enable assessment of complex systems which need simultaneous evaluation of multiple criteria. The research establishes new operational laws which extend the use of Fermatean fuzzy \(\ddot{Z}\) numbers to situations which demand flexible decision-making systems. The study investigates how to use Fermatean fuzzy \(\ddot{Z}\) numbers for assessing soccer player performance. The research investigates how well FF\(\ddot{Z}\)N Neutrality Aggregation Operators that evaluate goal scoring, assists, tackles, and passing accuracy can provide accurate performance rankings. The aggregation process uses expert evaluations which assess both positive and negative contributions to create an unbiased football player ranking system. The case study demonstrates how Fermatean fuzzy \(\ddot{Z}\) numbers can be used to make actual decisions. The process compares rankings produced by FF\(\ddot{Z}N\) Neutrality Aggregation Operators with WASPAS rankings to demonstrate how Fermatean fuzzy \(\ddot{Z}\) numbers help solve complex decision-making situations which need to manage uncertainty and multiple factors for optimal outcomes.
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Acknowledgements
1. This research was supported by the Doctoral Research Start-up Fund of Hubei University of Technology (XJ2023007801), the Hubei Provincial Natural. 2. Science Foundation (2025AFD653), the Wuhan Sport University ‘Donghu Scholar’ Programme (2023), the Hubei Provincial Higher Education Institutions Advantageous and Distinctive Disciplines (Clusters) ‘14th Five-Year Plan’ Special Fund (2021), and the Wuhan Sport University Middle-aged and Young Research Team (21KT17).
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Wei, Q., Yao, J. & Zheng, W. A decision aid approach for sports performance evaluation and player activity tracking using fermatean fuzzy Z-information. Sci Rep (2026). https://doi.org/10.1038/s41598-026-43693-4
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DOI: https://doi.org/10.1038/s41598-026-43693-4
