This paper considers the classical semiparametric partially linear model with exact inputs and interval-valued fuzzy outputs. For this purpose, the most commonly used classical two-phase procedure is extended to estimate an interval-valued fuzzy smooth function using nonparametric kernel methods at phase 1 and a least absolute deviation method at phase 2 to estimate the interval-valued fuzzy coefficients. A potential application of the proposed method is presented by a simulated data in hydrology study and an applied example. The proposed interval-valued semiparametric partially linear model is also examined to compare with the interval-valued fuzzy linear regression model via some extended goodness-of-fit criteria into the space of interval-valued fuzzy numbers.

中文翻译：

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具有精确输入和区间值模糊输出的线性模型

本文考虑具有精确输入和区间值模糊输出的经典半参数部分线性模型。为此，最常用的经典两阶段程序被扩展为在阶段 1 使用非参数核方法和在阶段 2 使用最小绝对偏差方法来估计区间值模糊平滑函数以估计区间值模糊系数。通过水文研究中的模拟数据和应用实例，展示了所提出方法的潜在应用。还检查了所提出的区间值半参数部分线性模型，以通过一些扩展的拟合优度标准到区间值模糊数空间与区间值模糊线性回归模型进行比较。