介绍模糊数学的基本概念，建立了用于缺陷模糊模式识别的两种数学模型，即模糊集法与模糊聚类法。

The concept of fuzzy mathematics is described and two fuzzy pattern recognition models of flaws based on fuzzy set method and fuzzy cluster method have been established.

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通过以全体样本对全体类别加权广义欧氏权距离平方和最小为目标函数，建立了模糊聚类、识别与优选决策统一的理论与循环迭代模型。

With the minimum square sum of weighted Euclidean distances as the objective function, the unified theory and cyclical iteration model of fuzzy cluster, recognition and optimum decision are founded.

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根据模糊聚类与模糊识别理论，基于模糊环境下的目标函数，提出了一种确定预报因子权重的理论模式。

According to fuzzy clustering theory and fuzzy pattern recognition theory, a theory and model deciding forecast factor weight was present on basis of fuzzy object function in this paper.

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