DEAR Model -The Theoretical Foundation

In this paper, we merge the differential equation model, regression model and credibility measure based fuzzy mathematics proposed by Liu [13] into a new differential equation associated regression model (abbreviated as DEAR model). The creation of the DEAR model does not only offer a rigorous treatment of the grey differential equation problem proposed by Deng [3] on the random fuzzy variable theoretical foundation, but also increases the variety of model choices greatly. Furthermore, we develop a multivariate DEAR model for the quantitative modeling based on multivariate small sample data. Multivariate DEAR models will be able to establish the quantitative relationship among the main response factor vectors and the covariate vectors, which is a major improvement of information extraction under sparse data availability. Finally, we point out some potential application areas of the new modeling family.