Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony

Abstract

Intuitionistic fuzzy sets are extended form of type 1 fuzzy sets. The modeling methods use intuitionistic fuzzy sets have second-order uncertainty approximation so these methods may have better results than methods based on type-1 fuzzy sets. Intuitionistic fuzzy sets have been used in forecasting methods and these methods are called intuitionistic fuzzy time series forecasting methods. In this study, new intuitionistic fuzzy time series definitions are made and a new forecasting method is proposed based on intuitionistic fuzzy sets. The first contribution of the paper is to make new fuzzy and intuitionistic fuzzy time series definitions. The second contribution is to make new forecasting model definitions for fuzzy and intuitionistic fuzzy time series. The last contribution is to propose a forecasting method for single-variable high-order intuitionistic fuzzy time series forecasting model. In the proposed method, fuzzification of observations is done by using intuitionistic fuzzy c-means algorithm and fuzzy relations are defined by pi-sigma artificial neural networks. Artificial bee colony algorithm is used to train Pi-Sigma artificial neural network in the proposed method. Real-world time series applications have been made for exploring performance of the proposed method.