Decomposition and Hierarchical Process for Fuzzy Cognitive Maps of Complex Systems

In order to reduce the scale and complexity, the decomposition methods of fuzzy cognitive maps for knowledge representation and reasoning are presented. Partition the vertices of original cognitive map into some groups, and then construct quotient cognitive map based on these groups. Thus, the analysis of the original FCM can be reduced to that of quotient FCM, which provides global information of original FCM, and some sub FCMs which keep an original topological structure and inference and provide local information of original FCM. It extremely reduces the original size and complexity, meanwhile, it is possible to study system at different slices and enhance the enrichment and flexibility of research between concepts. Some knowledge representations and reasoning of complex system use the method of hierarchical for fuzzy cognitive maps. Therefore, it highlights the hierarchical causal relationship and inclusion relationship between concepts, and embodies the space causal relation between concepts