摘要
利用矩阵半张量积理论,从两个方面对数量化理论(I)进行改进:一是改进模型,提出一种定性数据通用预测模型;二是扩展基准变量的维数,建立一种多维预测方法.首先,基于混合逻辑半张量积表示,研究一维基准变量预测问题,提出一种新的预测模型——伪混合逻辑函数模型,它可描述定量基准变量与定性说明变量间的任一复杂解析关系;并基于样品数据,研究如何确定预测模型的结构矩阵.然后,研究多维基准变量预测问题,提出一种伪混合逻辑函数向量预测模型,并给出其结构矩阵的确定方法.最后,给出一个应用例子,说明本文方法的有效性.
Quantification theory （Ⅰ） provides a kind of multi-ary analysis method for the forecast problem with its criterion variable quantitative and its explanatory variables qualitative. In such a theory, the forecast model is a one-dimensional linear one, which cannot be applied to high-dimension or nonlinear forecast problems. By the matrix semi-tensor product method, this paper improves quantification theory （Ⅰ） from two aspects： model and dimension. First, based on the algebraic expression of mix-valued logical variables, the forecast problem of one-dimensional criterion variable is investigated, and a new forecast model is presented. Second, we consider the multi-dimension forecast problem, and establish a new multidimension forecast method by using mix-valued logical function vectors. Finally, we give an illustrative example to demonstrate our new results.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2012年第7期1575-1581,共7页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(61074068
61034007)
高等学校博士点专项科研基金(G200804220028)
山东省自然科学基金(ZR2010FM013)
