Ranking Z-numbers Using the Optimal Clustering Method (CZ-number)

In recent years, modeling uncertainties through natural language has attracted growing attention, with Z-numbers, introduced by Zadeh in 2011, being a key concept. A Z-number consists of two fuzzy components: the first represents the possibility of an event’s occurrence, while the second expresses the probability of that occurrence. A major challenge in applying Z-numbers lies in properly structuring these two components; inappropriate strategies can lead to inaccurate results, especially in group decision-making contexts with large data volumes. To address this, the paper proposes an optimal clustering approach for structuring the components of Z-numbers more systematically and purposefully. This method enhances the accuracy of Z-number modeling by reducing errors in component formation. The effectiveness of the proposed approach is validated through a comparison with conventional fuzzy methods, demonstrating improved performance in handling uncertainty.