Interactively recurrent fuzzy functions with multi objective learning and its application to chaotic time series prediction

Fuzzy functions (FFs) models were introduced as an alternate representation of the fuzzy rule based approaches. This paper presents novel Interactively Recurrent Fuzzy Functions (IRFFs) for nonlinear chaotic time series prediction. Chaotic sequences are strongly dependent on their initial conditions as well as past states, therefore feed forward FFs models cannot perform properly. To overcome this weakness, recurrent structure of FFs is proposed by placing local and global feedbacks in the output parts of multidimensional subspaces. IRFFs' optimized parameters should minimize the output error and maximize clusters density. To achieve these contradictory goals, Non-dominated Sorting Genetic Algorithm II (NSGAII) is applied for simultaneously optimizing the objectives. Also, feedback loop parameters are tuned by utilizing gradient descent algorithm with line search strategy based on the strong Wolfe condition. The experimental setup includes comparative studies on prediction of benchmark chaotic sequences and real lung sound data. Further simulations demonstrate that our proposed approach effectively learns complex temporal sequences and outperforms fuzzy rule based approaches and feed forward FFs.