High order fuzzy time series forecasting method based on an intersection operation

The use of non-stochastic models such as fuzzy time series forecasting models for time series analysis has attracted the attention of researchers in recent years. Fuzzy time series forecasting models do not need strict assumptions, whereas conventional stochastic models need to satisfy some assumptions. In addition, fuzzy time series methods can be used if the observations of time series have uncertainty. Fuzzy time series approaches comprise three basic steps: fuzzification of the crisp observations, identification of fuzzy relations, and defuzzification. In previous studies, many methods have been proposed that allow all of these stages to obtain more accurate forecasting results. One of the weakest features of fuzzy time series methods is that the membership values are not considered in the forecasting process. This problem can be eliminated in first order approaches by using artificial neural networks to describe fuzzy relations. When determining the fuzzy relations, the membership values are not ignored if the inputs and outputs of the neural networks are the membership values for the periods t − 1 and t, respectively. However, the number of inputs of neural networks will increase greatly if this approach is extended to high-order models. Thus, it will be very difficult to train these neural networks. In this study, we propose a novel high-order fuzzy time series approach that considers the membership values, where artificial neural networks are employed to identify the fuzzy relations. In the proposed method, intersection operators are utilized to deal with an excessive number of inputs. In addition, the fuzzy c-means method is employed for fuzzification. The forecasting performance was evaluated by applying the proposed method to well-known time series data sets and the results obtained were compared with those produced by previously described forecasting methods. The superior performance of our proposed method was also supported by a simulation study