## Monthly Rainfall Forecasting Using High Order Singh’s Fuzzy Time Series Based on Interval Ratio Methods: Case Study Semarang City, Indonesia

Published: 2024-07-23

Page: 71-88

Erikha Feriyanto *

Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Indonesia.

Farikhin

Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Indonesia.

Nikken Prima Puspita

Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Indonesia.

*Author to whom correspondence should be addressed.

### Abstract

Aims: Sample: To determine the effectiveness of the proposed forecasting method, namely Singh's fuzzy time series based on high order (third order) interval ratios. And find out the forecasting results in January 2022.

Study Design:  Modification of Singh's fuzzy time series based on interval ratios.

Place and Duration of Study: Sample: monthly rainfall data for Semarang City from January 2017 to December 2021.

Methodology: The method proposed by the researcher is the Singh fuzzy time series forecasting method based on high order (third order) interval ratios. This research method uses a combination of Chen and Singh's fuzzy time series. Applying Chen's fuzzy time series in the section determining the universe of discourse () to fuzzification which includes determining the universe of discourse, determining interval partitions, forming Fuzzy Logical Relationships and Fuzzy Logical Relationship Groups. Then apply Singh's fuzzy time series to the forecasting part. Finally, calculate the Average Forecasting Error Rate (AFER) to test forecasting performance. In the forecasting part, it is obtained through a heuristic approach by building high order forecasting rules to obtain better results and have an effect on very small AFER values. In the step of determining the interval partition, this research uses the interval ratio method which aims to reflect variations in historical data.

Conclusion: Based on the calculation of the AFER value, the AFER for third order is 0.2422%. It can be said that Singh's fuzzy time series forecasting method based on high order (third order) interval ratios on monthly rainfall data for Semarang City from January 2017 to December 2021 is very good. And the rainfall forecast for January 2022 is 196.80 mm3 or into the category of very heavy rain.

Keywords: Forecasting, rainfall, fuzzy time series, interval ratio

#### How to Cite

Feriyanto, Erikha, Farikhin, and Nikken Prima Puspita. 2024. “Monthly Rainfall Forecasting Using High Order Singh’s Fuzzy Time Series Based on Interval Ratio Methods: Case Study Semarang City, Indonesia”. Asian Journal of Probability and Statistics 26 (8):71-88. https://doi.org/10.9734/ajpas/2024/v26i8638.