系数为LR-型模糊数的模糊Logistic回归模型的参数估计

Parameter Estimation of the Fuzzy Logistic Regressive Model with LR Typed Fuzzy Coefficients

摘要: 针对二分类变量问题，经典Logistic回归是合适的。由于观测结果的不精确，响应变量往往介于0，1之间，且没有概率分布，误差也不能完全看作随机性现象。为此，将经典Logistic回归模型与模糊集理论相结合，构建了具有清晰输入–模糊输出的一类模糊Logistic回归模型，其中系数与输出均用LR-型模糊数表示。用成功的可能性替代概率，这些可能性可以由一些语义词描述。然后基于截集构造了模糊数之间的距离，利用此距离得到了上述模型中模糊参数的最小二乘估计。最后将模型应用在狼疮中并通过相容性指数MSI = 0.54说明该模型的有效性。

Abstract: The classical logistic regression model is appropriate for the problems of binary variable. Since the observations were not crisp value, response variable was often between 0 and 1 and no probability distribution can be considered for response variable; hence error can not be completely regarded as random aspect. Therefore, by combining the classical logistic regression model with fuzzy sets theory, a fuzzy logistic regression model of crisp input and fuzzy output data is constructed; the coefficients and outputs are LR type fuzzy numbers. Considering the possibilities of success instead of the probabilities, the possibilities of success are described by some linguistic terms. Then the distance between two fuzzy numbers is constructed by cut sets. The least squares estimation of fuzzy parameters is obtained in proposed model based on the distance. Finally, the capability index MSI = 0.54 showed that the proposed model is effective of an ordinary one in the modeling Lupus.