Fuzzy Autoregressive Time Series Model Based on Symmetry Triangular Fuzzy Numbers

Abstract

The symmetry triangular fuzzy number has been developed to build fuzzy autoregressive models by using various approaches such as low-high data, integer number, measurement error, and standard deviation data. However, most of these approaches are not simulated and compared between ordinary least square and fuzzy optimization in parameter estimation. In this paper, we are interested in implementation of measurement error and standard deviation data in construction symmetry triangular fuzzy numbers. Additionally, both types of triangular fuzzy numbers are deployed to build a fuzzy autoregressive model, especially the second order. The simulation result showed that the fuzzy autoregressive model produced the smaller mean square error and average width if compared with the ordinary autoregressive model. In the implementation, the high accuracy was also achieved by the fuzzy autoregressive model in consumer goods stock prediction. From the simulation and implementation, the proposed fuzzy autoregressive model is a competent approach for upper and lower forecasts.