Picture fuzzy time series: Defining, modeling and creating a new forecasting method

The extant literature has shown that fuzzy sets can be applied to solve forecasting problems. A fuzzy time series is a kind of time series whose observations are fuzzy sets or fuzzy numbers. A picture fuzzy set is a generalized form of fuzzy and intuitionistic fuzzy sets that is also referred to as a standard neutrosophic set. In this study, a picture fuzzy time series and a single variable high order picture fuzzy time series forecasting model are defined based on picture fuzzy sets. We also propose a new picture fuzzy time series forecasting method. The proposed method solves the issues inherent in the high order single variable picture fuzzy time series forecasting model. The proposed method has three basic steps: (1) picture fuzzification, (2) model construction, and (3) forecasting. In the proposed method, picture fuzzification is accomplished via picture fuzzy clustering, and positive, neutral and negative membership values are obtained. The model construction step consists of estimating a function. This study employed a pi-sigma artificial neural network for this estimation. The proposed method is applied to a meteorological data set with an expanding window approach. The proposed method outperforms recent fuzzy time series and classical methods found in the extant literature.