A New Multi-Step Backward Cloud Transformation Algorithm Based on Normal Cloud Model

The representation and processing of uncertainty information is one of the key basic issues of the intelligent information processing in the face of growing vast information, especially in the era of network. There have been many theories, such as probability statistics, evidence theory, fuzzy set, rough set, cloud model, etc., to deal with uncertainty information from different perspectives, and they have been applied into obtaining the rules and knowledge from amount of data, for example, data mining, knowledge discovery, machine learning, expert system, etc. Simply, This is a cognitive transformation process from data to knowledge (FDtoK). However, the cognitive transformation process from knowledge to data (FKtoD) is what often happens in human brain, but it is lack of research. As an effective cognition model, cloud model provides a cognitive transformation way to realize both processes of FDtoK and FKtoD via forward cloud transformation (FCT) and backward cloud transformation (BCT). In this paper, the authors introduce the FCT and BCT firstly, and make a depth analysis for the two existing single-step BCT algorithms. We find that these two BCT algorithms lack stability and sometimes are invalid. For this reason we propose a new multi-step backward cloud transformation algorithm based on sampling with replacement (MBCT-SR) which is more precise than the existing methods. Furthermore, the effectiveness and convergence of new method is analyzed in detail, and how to set the parameters m, r appeared in MBCT-SR is also analyzed. Finally, we have error analysis and comparison to demonstrate the efficiency of the proposed backward cloud transformation algorithm for some simulation experiments.