Hesitant fuzzy time series forecasting model of higher order based on one and two-factor aggregate logical relationship

Abstract

Fuzzy time series forecasting is a methodology that incorporates fuzzy logic to handle uncertainty in time series data. It allows for more flexible and accurate predictions by considering the linguistic terms and membership functions associated with each data point, enabling a better representation of complex patterns and trends within the time series. A time series forecasting model examines the relationships between present and past observations for future measurement. This article proposes a hesitant fuzzy time series forecasting (FTSF) technique for higher order based on one and two-factor aggregate fuzzy relationships. The proposed method presents a new approach to partitioning intervals into an unequal and equal length. The hesitant fuzzy sets are defined for each observation, and fuzzification is based on their maximum score function. Further, aggregated triangular fuzzy numbers are defined using an aggregation operator corresponding to the fuzzified datum. In order to enhance forecasting performance, this work also introduces a novel defuzzification rule based on aggregated fuzzy logical relationship groups (AFLRGs) for higher order one and two-factor fuzzy time series. The implementation of the proposed approach is verified on two data sets to the forecasting of enrollment data and TAIFEX and TAIEX stock index data sets, and the forecasting error is tested in term of different statistical parameters. Thus, the model validates the effectiveness of the proposed method with higher forecasting accuracy rate in the environment hesitant fuzzy information.