Design And Implementation Of Type-2 Fuzzy Cognitive Map

Fuzzy cognitive map(FCM)has intuitive and flexible knowledge representation,strong ability of fuzzy reasoning,and close connection with neural networks,graph theory and other fields,making it widely used in many research areas.However,the traditional FCM also has some drawbacks: On one hand,the construction process of FCM relies too much on domain expert knowledge.Because expert knowledge has strong subjectivity and limitations,the FCM model construction is not accurate and reliable;On the other hand,in traditional FCM and its various improved models,causality between concepts uses a “precise” value to express causal effects,and doesn't consider the uncertainty of the causal relationship between concepts.To solve the above problems,this paper proposes a Type-2 fuzzy cognitive map model.This model uses fuzzy neural network self-learning features to automatically identify membership functions and quantify the causal relationships between concepts without the need for expert knowledge pre-assignment,which greatly reduces manual intervention and improves FCM's learning ability.In the fuzzy neural network model,the mutual causality between concepts is defined by mutual subsethood,which gives a more transparent and reasonable mathematical explanation and reasoning process.At the same time,the Type-2 fuzzy set is the theory that expresses the uncertainty of fuzzy semantics.Therefore,this paper introduces it to solve the uncertainty problem of the causality between concepts in FCM,and then integrates the theory into the fuzzy neural network,which makes the model has stronger expressive ability in fuzzy semantics.Subsequently,this paper introduces the structure and function of neural network in each layer of the new model in detail,and gives a detailed mathematical reasoning process.The learning and training of the model uses the Backpropagation Network,which includes two processes: forward signal propagation and error back propagation.The back-propagation process uses a gradient descent algorithm to perform feedback adjustments and update parameters,and gives a detailed partial derivative calculation inference process.Through iterative training,the model parameters are continuously fed back and adjusted until the model reaches the minimum error.The training is completed.The Type-2 fuzzy cognitive map model presented in this paper has stronger learning,reasoning ability and the ability of express the fuzzy semantic uncertainty than the traditional FCM model,which makes the inference process of model more accurate,and has higher fault tolerance and stronger applicability.Through comparative experiments,it is proved that the model has better prediction effect and performance on time series problems than other fuzzy systems and neural network models.