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基于Choquet积分的非线性回归模型研究
Discussion of the Nonlinear Multiregressions Model Based on Choquet Integral
【作者】 周翠莲；
【作者基本信息】 河北大学 ， 基础数学， 2009， 硕士
【摘要】 回归模型的建立是回归分析的首要问题。由于Choquet积分中所采用的非可加集函数能够描述属性间的交互作用,所以基于Choquet积分的非线性回归模型在应用于一些实际问题时,取得了很好的效果。在现有的非线性回归模型中,非线性积分所采用的非可加集函数一般是定义在有限论域上的实值集函数。但在一些实际问题中,集函数取区间数或者模糊数更加合理。本文设计了一种基于关于区间值带符号模糊测度的Choquet积分的非线性回归模型。其中,关于区间值带符号模糊测度的Choquet积分(CIIM)的值可以采用线性规划的方法计算。另外,模型中的参数通过一种进化算法—混合蛙跳算法优化确定,实验结果验证了算法的可行性与有效性。
【Abstract】 Establishment of regression model is an important part of regression analysis. The nonlinear multiregression models based on Choquet integrals have shown successful applications in practice since the adopted nonadditive set functions in Choquet integrals can effectively describe interaction among the attributes invovled. In the existing nonlinear multiregressin models, the nonlinear integrals are with respect to real-valued set functions. However, in some real problems, it seems more reasonable that the set functions are interval or fuzzy numbers. In this paper, a nonlinear multiregression model is designed based on Choquet integral with respect to an interval-valued signed fuzzy measure. The generalized Choquet integral in the model can be calculated by Linear Programming. Furthermore, we determine the regression coefficients optimally using a population evolutionary algorithm. Experimental results demonstrate the feasibility and effectiveness of the algorithm.
【Key words】 Fuzzy measure； Choquet integral； Interval-valued； Linear Programming； Multiregression model；