A High-Order Neutrosophic-Neuro-Gradient Descent Algorithm-Based Expert System for Time Series Forecasting

Abstract

This article proposed a novel hybrid time series forecasting model using neutrosophic set (NS) theory, artificial neural network (ANN) and gradient descent algorithm. This study deals with three main problems of time series dataset, viz., representation of time series dataset using NS, three degrees of memberships of NS together, and generation of the forecasting results. To resolve these three domain specific problems, this study advocated the application of neutrosophic-neuro-gradient approach. NS theory was utilized to represent the uncertainty associated with time series dataset and was referred to as neutrosophic time series (NTS). In NTS, various decision rules were created in the form of IF-THEN rules, which were termed as neutrosophic entropy decision rules (NEDRs). An ANN-based architecture took NEDRs as input to evolve the forecasting results. To improve the performance of ANN and to obtain optimal forecasting results, this study additionally utilized the gradient descent algorithm to minimize the differences between the calculated and target output values during the simulation. The proposed model was verified and validated with three different datasets, including TAIFEX index, university enrollment dataset of Alabama and Taiwan Stock Exchange Corporation (TSEC) weighted index. Experimental results showed that the proposed model outperformed existing benchmark models with average forecasting error rates of 1.02%, 0.74% and 1.27% for the TAIFEX, university enrollment and TSEC, respectively.