The implementation of the optimal rule bases generated by hybrid fuzzy c-mean and particle swarm optimization

The aims of the paper are to generate fuzzy rule bases that be optimized through fuzzy c-means (FCM) and particle swarm optmization (PSO), and to develope the fuzzy inference systems (FIS) that have the system inputs are combination between the number of linguistic values and the number of assumed lags influence to the system output. The outputs of FCM including are the cluster centers and partition matrix. The number of rules in the fuzzy rule bases formed by FCM is the same as the number of clusters. The cluster centers are used as the center parameters of the Gaussian membership function (MF), while the elements of partition matrix are used to determine the optimal spread parameters of Gaussian's MF through PSO algorithm. The identification of system input variables is done using plot partial autocorrelation function (PACF). The formation of a tentative model based on significant PACF values to construct the input-output pairs matrix which is subsequently grouped by using FCM. The implementation of FIS uses the exchange rate of USD to IRD dataset that is obtained four significant PACF values on lags of k = 1, 5, 8, and 10 which are subsequently used as input variables. Based on the four input variables, systems with 2 inputs, 3 inputs, and 4 inputs combined with the number of clusters of n = 3, 5, and 7 formed 21 systems. Based on the values of both MAPE and R² that is obtained the result that in training data if the number of input variables and number of clusters are increased then the system has the better performance, but in the testing data, the system performance decresed when the number of input variables and the number of clusters.are increased. The best performing system is the system with 2 inputs and 5 clusters.