Trapezium Cloud Decision-Making Method with Probabilistic Multi-Granularity Symmetric Linguistic Information and Its Application in Standing Timber Evaluation

It is crucial to evaluate the quality of standing timber for the rational and effective management of forest land. In practice, it is often difficult to obtain accurate data on various indicators of standing timber due to constraints such as measurement conditions, accuracy, and cost. Therefore, this study developed a multi-attribute decision-making method based on trapezium clouds and applied it to evaluate the standing timber quality of forest land. Firstly, a trapezium cloud transformation method was designed to handle multi-granularity symmetric linguistic information problems caused by different knowledge backgrounds of decision-makers, and the symmetric structure inherent in trapezium clouds helped to ensure the balanced processing of information from various asymmetric cognitive perspectives. Secondly, a trapezium cloud generalized weighted Heronian mean was proposed for the information aggregation process of trapezium clouds. Then, the concept of trapezium cloud interval similarity was defined, and an optimization model was constructed to determine the normalized interval weights of attributes. Based on the symmetric numerical feature, the calculation formula for the approximate centroid coordinates of trapezium clouds was derived, and based on this, the ranking method of trapezium clouds was obtained. Finally, taking the evaluation of standing timber quality in forest land as a numerical example, the applicability of the constructed multi-attribute decision-making method was demonstrated. In addition, the corresponding comparison analysis verified the superiority and effectiveness of the proposed method.