Picture fuzzy regression functions approach for financial time series based on ridge regression and genetic algorithm

Recent years, fuzzy inference systems are efficient tools for solving forecasting problems. Fuzzy inference systems are based on fuzzy sets and use membership values besides original data so a data augmentation mechanism is employed in the fuzzy inference. Picture fuzzy sets provide additional information to original data via positive degree membership, negative degree membership, neutral degree membership and refusal degree membership apart from fuzzy sets. The data augmentation with this additional information will be provided to build a better inference system than fuzzy inference systems. In this study, picture fuzzy inference system is proposed for forecasting purpose by using ridge regression and genetic algorithm. Ridge regression method is used to obtain picture fuzzy functions and genetic algorithm is used to emerge different information coming from systems which are designed for positive degree membership, negative degree membership and neutral degree membership. In the proposed method, picture fuzzification is provided by picture fuzzy clustering. The proposed inference system is tested by various stock exchange data sets. The forecasting of the proposed method is compared with well-known forecasting methods. The obtained results are evaluated according to different error measures such as root of mean square error and mean of absolute percentage error.