TY - JOUR

T1 - Picture fuzzy time series

T2 - Defining, modeling and creating a new forecasting method

AU - Egrioglu, Erol

AU - Bas, Eren

AU - Yolcu, Ufuk

AU - Chen, Mu Yen

PY - 2020/2/28

Y1 - 2020/2/28

N2 - 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.

AB - 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.

KW - Forecasting

KW - Pi-sigma artificial neural networks

KW - Picture fuzzy C-means

KW - Picture fuzzy sets

KW - Picture fuzzy time series

U2 - 10.1016/j.engappai.2019.103367

DO - 10.1016/j.engappai.2019.103367

M3 - Journal article

AN - SCOPUS:85075122917

VL - 88

JO - Engineering Applications of Artificial Intelligence

JF - Engineering Applications of Artificial Intelligence

SN - 0952-1976

M1 - 103367

ER -