Z-number linguistic term set for multi-criteria group decision-making and its application in predicting the acceptance of academic papers

Real-world information is often characterized by uncertainty and partial reliability, which led Zadeh to introduce the concept of Z-numbers as a more appropriate formal structure for describing such information. However, the computation of Z-numbers requires solving highly complex optimization problems, limiting their practical application. Although linguistic Z-numbers have been explored for their computational straightforwardness, they lack theoretical support from Z-number theory and exhibit certain limitations. To address these issues and provide theoretical support from Z-numbers, we propose a Z-number linguistic term set to facilitate more efficient processing of Z-number-based information. Specifically, we redefine linguistic Z-numbers as Z-number linguistic terms. By analyzing the hidden probability density functions of these terms, we identify patterns for ranking them. These patterns are used to define the Z-number linguistic term set, which includes all Z-number linguistic terms sorted in order. We also discuss the basic operators between these terms. Furthermore, we develop a multi-criteria group decision-making (MCGDM) model based on the Z-number linguistic term set. Applying our method to predict the acceptance of academic papers, we demonstrate its effectiveness and superiority. We compare the performance of our MCGDM method with five existing Z-number-based MCGDM methods and eight traditional machine learning clustering algorithms. Our results show that the proposed method outperforms others in terms of accuracy and time consumption, highlighting the potential of Z-number linguistic terms for enhancing Z-number computation and extending the application of Z-number-based information to real-world problems.