Presenting a Fuzzy Approach to Optimize Predicting High Order Time Series

It is difficult to apply the real world’s conceptions due to their uncertainty. Generally, time series are known to be non-linear or non-stationary. Regarding these two features, a system should be sensitive enough to apply the unity of time series and repeat this sensitiveness in the prediction. A predict system can exactly scrutinize the hidden features of time series and also can have high predicting runs. Lots of statistical tools such as regression analysis, gradient average, exponential gradient average and auto regression gradient average are used in traditional predictions. One of the biggest challenges of these approaches is the necessity of greater observations and the avoidance of linguistic variables or subjective experts’ ideas. Also these methods are limited to linear being assumptions. In order to dominate the limitations of traditional methods, many researchers have utilized soft computations like fuzzy logic, fuzzy neural networks, evolutionary algorithms and etc.
In this paper, we proposed a new fuzzy prediction novel based on the high order fuzzy time series. Our proposed model is based on the higher order fuzzy time series prediction computational approach. In this method a group of features are evaluated, by adding the value of the preceding element of predicting element to the result of the series’ differences. At that, particle swarm optimization is used to optimize Calculation algorithm features, which renders a better performance in order to solve the problems of higher order fuzzy time series. Then by choosing the best features, a result can be inferred as the predicting value.
The performance of the approach is presented in which after the fuzzification of time series and creating the logical fuzzy relations, by using the lower limit of the predicting element’s range and its consecutive range, and the resulted difference of sequential elements, some specific computations are done and a set of features are gained. Then, using the particle swarm optimization function, the best parameter is selected. The fitness function in the proposed method has two parts: a general section (the average of all orders) and a partial (Every columns orders). In general section, the overall average of error is shown. In Every columns orders section each column individually considered. For the second to tenth order (9 PSO separate) the answer is checked. The method is as follow; we used two parameters b and d for the feature calculation algorithm. The amount of d was manually and randomly between 3 – 1000, but PSO find the amount of b.
Properties obtained by this method, have less outliers data and waste, which it causes predicted closer, with less error.
Finally, defuzzification is performed. The yielded score is the predicted integer value of considered element.
In order to decide the precision of the prediction’s rate, we compare the proposed model to other methods using the mean square error and the average error. In order to show the efficiency of the proposed approach, we have implemented this method on the Alabama University’s enrollment database. It can be observed that the suggested method provides better results compared to the other methods and also renders a lower error.