Introducing polynomial fuzzy time series

Using polynomial concept and non-liner optimization enhanced the performance of Chen's (1996) and Yu's (2005b) methods as the two frequently used methods in fuzzy time series model. To this end, polynomial schemes were given to each fuzzy logical relationship groups that had been established through forecast process to establish non-linear optimization systems. The optimal solutions of this system were applied in corresponding steps of algorithms to obtain new weights. To validate model reliability and its effectiveness, the forecasts of two huge databases namely 5 years Taiwan's stock index and 2010 load data of Power Supply Company in Johor Bahru in Malaysia were then exposed to the proposed model. Next, the forecasts were compared with real values in testing datasets. The evaluation of measuring criteria namely RMSEs and MAPEs showed that the proposed model could produce accurate forecast compared with the Chen's and Yu's method in fuzzy time series. The implication of this study is to generalize the results to other fuzzy time series models.