High-order Intuitionistic Fuzzy Cognitive Map Based on Evidential Reasoning Theory

An intuitionistic fuzzy cognitive map (IFCM) is an extension of a fuzzy cognitive map (FCM) that forms a graph-oriented fuzzy map describing both causal relationships between pairs of concepts and the states of concepts via intuitionistic fuzzy sets (IFSs). In contrast with an FCM, an IFCM provides much more flexibility in system modeling. However, IFCMs may lead to confusing or unreasonable results in system modeling since they do not fully consider the negative influence from conventional operations on IFSs, the activation process of concepts, and the problem of aggregating knowledge with different importance levels. To solve the challenges of IFCMs, we propose a high-order IFCM based on evidential reasoning (ER) (IFCMR) theory in this study. First, we introduce an evidential intuitionistic fuzzy aggregation (EIFA) operator and a multiplication operation on IFSs using an ER theory. Second, we establish the theory of IFCMR based on the EIFA operator and the newly introduced multiplication operation on IFSs. Third, we propose a scheme of aggregating IFCMRs with different importance levels using the EIFA operator, which can also be utilized to aggregate conflict knowledge and to determine objective connections in terms of an evidential cognitive map (ECM). Finally, several numerical and practical examples are employed to test and verify the feasibility and validity of IFCMRs in comparison with both IFCMs and ECMs.