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.

Automated summary

The study aims to address the challenge of obtaining accurate results when using the GM(1,1) model for fitting and predicting approximate non-homogeneous exponential sequences by developing a fuzzy GM(1,1) model (FGM) that combines Grey Theory and Credibility Theory. The FGM introduces double exponential fuzzy numbers and their membership functions, utilizing Credibility Theory to calculate the expectation of fuzzy variables, resulting in unbiased results for the tight non-homogeneous exponential sequences. The effectiveness, feasibility, and optimization of the FGM(1,1) model are illustrated through empirical and numerical case studies.