New Mechanisms for Reasoning and Impacts Accumulation for Rule-Based Fuzzy Cognitive Maps

Rule-based fuzzy cognitive maps (RBFCMs) have been developed for modeling nonmonotonic, uncertain, cause-effect systems. However, the standard reasoning and impact accumulation mechanisms developed for RBFCMs assume that the level of variation that a fuzzy set represents is directly linked with the shape of the fuzzy set. It poses a big restriction on how the corresponding fuzzy sets have to be constructed. In this paper, we propose a new reasoning and impact accumulation mechanisms which take into consideration standard semantics of fuzzy sets, where their uncertainty is measured by fuzziness. New type of complex fuzzy relationships and reasoning on them is introduced to model a joint impact of several causal nodes on one effect node. With these new mechanisms, RBFCMs become much more flexible, provide more means to capture complexity of real-world systems, and are less computational demanding than standard mechanisms. The advantages of the new RBFCMs are demonstrated using different examples and compared with standard mechanisms.