Fuzzy Grey Model for Forecasting Non-homogeneous Exponential Sequence

Getting accurate results when GM (1, 1) model is used for fitting and predicting approximate non-homogeneous exponential sequence, is a challenge. We sought to address this issue by combining Grey Theory and Credibility Theory, to develop a fuzzy GM (1, 1) model (FGM), which introduces the double exponential fuzzy numbers and its membership function. The expectation of fuzzy variables for replacing the non-homogeneous exponential sequence was calculated by Credibility Theory, i.e. the homogeneous process. The novel method yields unbiased results when used in fitting and predicting the tight non-homogeneous exponential sequence. Finally, we use an empirical case and a numerical sequence case to illustrate the effectiveness, feasibility, and optimization of the FGM (1, 1) model.