Fuzzy regression is a generalized regression model to represent the relationship between dependent and independent variables in a fuzzy environment. The fuzzy linear regression analysis seeks for regression models fitting well all the data based on a specific criterion. In this paper, an adaptive neuro-fuzzy inference system (ANFIS) is employed for the analysis and prediction of a nonparametric fuzzy regression function with non-fuzzy inputs and symmetric trapezoidal fuzzy outputs. To this end, two new hybrid algorithms are proposed in which the fuzzy least squares and linear programming have been used to optimize the secondary weights. The algorithms are applied to a multi-layered validation method to confirm the models’ reliability. In addition, three methods of nonparametric fuzzy regression with crisp inputs and asymmetric trapezoidal fuzzy outputs, are compared. Three nonparametric techniques in statistics, namely local linear smoothing (L-L-S), K-nearest neighbor smoothing (K-NN) and kernel smoothing (K-S) with trapezoidal fuzzy data have been analyzed to obtain the best smoothing parameters. The performance of the models is illustrated through numerical examples and simulations. More specifically, the accuracy of the algorithms is confirmed by exhaustive simulations.

模糊回归是一种广义回归模型，用于表示模糊环境中因变量和自变量之间的关系。模糊线性回归分析寻求基于特定准则的拟合所有数据的回归模型。本文采用自适应神经模糊推理系统（ANFIS）对具有非模糊输入和对称梯形模糊输出的非参数模糊回归函数进行分析和预测。为此，提出了两种新的混合算法，其中使用了模糊最小二乘和线性规划来优化次级权重。该算法被应用于多层验证方法，以确认模型的可靠性。此外，比较了具有明晰输入和非对称梯形模糊输出的三种非参数模糊回归方法。分析了统计中的三种非参数技术，即局部线性平滑（LLS），K最近邻平滑（K-NN）和带有梯形模糊数据的核平滑（KS），以获得最佳平滑参数。通过数值示例和仿真说明了模型的性能。更具体地，通过详尽的仿真来确认算法的准确性。通过数值示例和仿真说明了模型的性能。更具体地，通过详尽的仿真来确认算法的准确性。通过数值示例和仿真说明了模型的性能。更具体地，通过详尽的仿真来确认算法的准确性。