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This paper proposes an evolutionary computing based automatic partitioned clustering of probability density function, the so-called binary adaptive elitist differential evolution for clustering of probability density functions (baeDE-CDFs). Herein, the k-medoids based representative probability density functions (PDFs) are preferred to the k-means one for their capability of avoiding outlier effectively. Moreover, addressing clustering problem in favor of an evolutionary optimization one permits determining number of clusters “on the run”. Notably, the application of adaptive elitist differential evolution (aeDE) algorithm with binary chromosome representation not only decreases the computational burden remarkably, but also increases the quality of solution significantly. Multiple numerical examples are designed and examined to verify the proposed algorithm’s performance, and the numerical results are evaluated using numerous criteria to give a comprehensive conclusion. After some comparisons with other algorithms in the literature, it is worth noticing that the proposed algorithm reveals an outstanding performance in both quality of solution and computational time in a statistically significant way.

This paper proposes the forecasting model for the fuzzy time series based on the improvement of the background data and fuzzy relationship (IFTC). This algorithm is built based on the fuzzy cluster analysis which the suitable number of clusters for series is considered. The problem of interpolating data according to fuzzy relationships of time series in the trapezoidal fuzzy number is also established. The proposed model is illustrated step by step by a numerical example and effectively implemented by the Matlab procedure. The IFCT has advantages in comparing to other models via the several indexes such as the MAE, MAPE and MSE with the Enrollment dataset.