The cross-association relation based on intervals ratio in fuzzy time series

Abstract

The fuzzy time series (FTS) is a forecasting model based on linguistic values. This forecasting method was developed in recent years after the existing ones were insufficiently accurate. Furthermore, this research modified the accuracy of existing methods for determining and the partitioning universe of discourse, fuzzy logic relationship (FLR), and variation historical data using intervals ratio, cross association relationship, and rubber production Indonesia data, respectively. The modified steps start with the intervals ratio to partition the determined universe discourse. Then the triangular fuzzy sets were built, allowing fuzzification. After this, the FLR are built based on the cross-association relationship, leading to defuzzification. The average forecasting error rate (AFER) was used to compare the modified results and the existing methods. Additionally, the simulations were conducted using rubber production Indonesia data from 2000-2020. With an AFER result of 4.77%<10%, the modification accuracy has a smaller error than previous methods, indicating very good forecasting criteria. In addition, the coefficient values of D₁ and D₂ were automatically obtained from the intervals ratio algorithm. The future works modified the partitioning of the universe of discourse using frequency density to eliminate unused partition intervals.