Average-Based Fuzzy Time Series Markov Chain Based on Frequency Density Partitioning

Abstract

Fuzzy time series (FTS) is one of the forecasting methods that has been developed until now. The fuzzy time series is a forecasting method that uses the concept of fuzzy logic, which Song and Chissom first introduced. The fuzzy time series (FTS) Markov chain uses the Markov chain in defuzzification. The determination of the length of the interval in the fuzzy time series plays an important role in forming a fuzzy logic relationship (FLR), and this FLR will be used to determine the forecasting value. One method that can be used to determine the interval length is average-based. However, several studies use partitioning based on frequency density to obtain the optimal interval length to get better forecasting accuracy. This study combines the fuzzy time series Markov chain, Average-based fuzzy time series, and Fuzzy time series based on frequency density partitioning to become average-based fuzzy time series Markov chain based on the Frequency Density Partition which conducts redivided intervals based on frequency density in the average-based fuzzy time series Markov chain method. This method is implemented in forecasting the Indonesian Islamic stock index (ISSI) for the selected period. The calculation of the accuracy level using the mean square error (MSE) and the mean average percentage error (MAPE) shows that the fuzzy Markov chain-based fuzzy time series based on the frequency density partition has a high level of accuracy in forecasting.

Ratio Interval-Frequency Density with Modifications to the Weighted Fuzzy Time Series

“…The FTS was first presented by Song & Chissom (1993), and since then, it has seen a lot of development, including interval ratio (Huarng & Yu, 2006;Haikal et al, 2022;Vianita et al, 2023), frequency density partitioning (Hariyanto et al, 2023;Irawanto et al, 2019;Jilani et al, 2007;Mukminin et al, 2021), the weighted FTS (Jiang et al, 2017;Yu, 2005). Forecasting model uses first-order (Lu et al, 2015;Mirzaei Talarposhti et al, 2016;Singh & Borah, 2013) or highorder (Lu et al, 2015;Mirzaei Talarposhti et al, 2016;Singh & Borah, 2013) methods.…”

“…Interval ratio Huarng & Yu (2006); Haikal et al (2022); Vianita et al (2023) and frequency density partitioning (Hariyanto et al, 2023;Irawanto et al, 2019;Jilani et al, 2007;Mukminin et al, 2021) in fuzzy relationships that were consistently disregarded. In Yu (2005) studied that forecasting must devote responsibility for recurring fuzzy connections and provide varied weights to different fuzzy interactions.…”