Abstract: The conventional Fuzzy Cognitive Maps (FCM) can only represent monotonic or symmetric causal relationships, but can not simulate the AND／OR relationships among the antecedent nodes. The Hybrid Fuzzy Cognitive Map (HFCM) is proposed to eliminate the drawbacks of the existing FCM models. The HFCM represents the casual relationships with single-antecedent fuzzy rules to enhance linguistic information and simulative capability of FCM, and simulates various AND／OR relationships among the antecedent nodes by aggregating causal inference results with Weighted Ordered Weighted Averaging(WOWA) or Ordered Weighted Averaging(OWA) operators. Compared with the conventional FCM, the HFCM has more powerful cognitive capability. Compared with the Rule Based Fuzzy Cognitive Map, the HFCM avoids the combinatorial rule explosion problem as the scale and complexity of its rule base are reduced from the geometrical level to the arithmetical level, and improves the representation and inference performance of FCM. The HFCMs combine the advantages of numeric FCMs and linguistic FCMs.

Key words: fuzzy cognitive map, weighted ordered weighted averaging operator, fuzzy rule, AND/OR relationship, ordered weighted averaging operator