Univariate DEMR model — The formation and foundation

In this paper, we propose and develop a differential equation motivated regression model, abbreviated as DEMR model, which has a random fuzzy error structure for the facilitation of the modeling challenges facing small sample uncertainty, model translation caused misspecification uncertainty, and random sampling uncertainty. Different from common regression models as well as the one-variable first order grey differential equation model, abbreviated as GM(1,1) proposed by Deng (1983), DEMR is established on a rigorous mathematical foundation founded by Liu [4] and expecting to receive a full acceptance in research community.