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The fuzzy cognitive map (FCM) has gradually emerged as a powerful paradigm for knowledge representation and a simulation mechanism that is applicable to numerous research and application fields. However, since efficient methods to determine the states of the investigated system and to quantify causalities that are the very foundations of FCM theory are lacking, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to the model subjectivity and difficulties with assessing its reliability. In this paper, we proposed a fuzzy neural network to enhance the learning ability of FCMs. Our approach incorporates the inference mechanism of conventional FCMs with the determination of membership functions, as well as the quantification of causalities. In this manner, FCM models of the investigated systems can automatically be constructed from data and, therefore, operate with less human intervention. In the employed fuzzy neural network, the concept of mutual subsethood is used to describe the causalities, which provides more transparent interpretation for causalities in FCMs. The effectiveness of the proposed approach in handling the prediction of time series is demonstrated through many numerical simulations.Index Terms-Fuzzy cognitive maps (FCMs), fuzzy neural network, fuzzy-rule identification, mutual subsethood.

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