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基于可能性理论的可能性线性模型(PLM)在模糊建模等应用中有重要的作用.本文首先借鉴统计学习理论将此模型扩展为正则化(regularized)的可能性线性模型(RPLM),以提高其泛化能力.然后利用将其优化问题转换为最大后验估计问题的新方法,研究当数据含有噪声时,模型中的拟合门限值λ和输入噪声均方差σ之间的关系.理论推导和仿真实验均证明,当输入噪声为高斯模型时,λ和σ成近似的线性反比关系.该结论对 PLM 和RPLM 均有借鉴意义,为已知输入噪声均方差时,合理选择λ提供理论依据.
Possibilities Based on Possibility Theory Linear models (PLMs) play an important role in applications such as fuzzy modeling.Firstly, this paper expands the model to a regularized possibility linear model (RPLM) based on statistical learning theory, And then use the new method to convert the optimization problem to the maximum a posteriori estimation problem to study the relationship between the fitting threshold λ and the mean square error σ of the input noise when the data contains noise. Both theoretical derivation and simulation experiments prove that when the input noise is a Gaussian model, λ and σ become linear approximation inversely proportional to each other. This conclusion is of great significance to both PLM and RPLM, and provides a reasonable choice of λ for the known input noise mean-squared error Theoretical basis.