A high-order multi-variable Fuzzy Time Series forecasting algorithm based on fuzzy clustering

A High-order algorithm for Multi-Variable Fuzzy Time Series (HMV-FTS) is presented based on fuzzy clustering to eliminate some well-known problems with the existing FTS algorithms. High-order algorithms can handle only one-variable FTS and multi-variable algorithms can handle only one-order FTS. HMV-FTS does both tasks simultaneously. FTS algorithms cannot incorporate existing information about future value of a variable in the forecasting process while HMV-FTS can. Defuzzification of the fuzzy value of a forecast to cluster centers or midpoint of intervals and use of intervals are other controversial problems with the existing FTS algorithms. These are eliminated by constructing fuzzy sets from partition matrices and letting each data point to contribute in defuzzification based on its membership grade in the fuzzy sets. In multi-variable FTS algorithms, one variable is considered as main variable which is forecasted and the other variables are secondary; while HMV-FTS treats all variables equally and more than one variable can be forecasted at the same time. It is shown that HMV-FTS is suitable for system identification, forecasting and interpolation. This algorithm is more accurate than popular FTS algorithms and other forecasting tools and systems such as ANFIS, Type II fuzzy model and ARIMA model.