Backward cloud transformation algorithm based on Kullback Leibler divergence

As a bidirectional cognitive model for dealing with uncertainty, cloud model (CM) are commonly used in application scenarios such as fault diagnosis, system modeling, and evaluation. CM achieves bidirectional conversion between qualitative concepts and quantitative values through forward cloud transformation (FCT) and backward cloud transformation (BCT) algorithms. Among them, the BCT algorithm obtains key parameters that characterize the randomness and fuzziness of concepts through the analysis of quantitative sample data, namely the expectation (Ex), entropy (En), and hyper entropy (He) for CM. However, the existing BCT algorithms adopt an integrated modeling approach, ignoring the impact of data with different distribution characteristics on obtaining key parameters for CM. Therefore, this paper proposes a BCT algorithm based on Kullback Leibler (KL) divergence, aiming to refine the process for obtaining key parameters of CM by analyzing the distribution differences between sample data. Firstly, the corresponding atomization template dataset (ATD) is obtained by conducting a coarse-grained analysis of the sample data. Then, calculate the KL divergence between sample data and ATD to effectively evaluate the atomization state of CM after transforming the sample data. Based on the evaluation results, two differentiated BCT strategies are designed for both atomization and non-atomization states to obtain key parameters of CM. Finally, a comparative analysis is conducted between the proposed method and traditional BCT algorithms, using the University of California Irvine (UCI) benchmark dataset and real fault diagnosis data for error analysis. The experimental results indicate that the proposed method can obtain more accurate key parameters of CM than other BCT algorithms.