回归分析是现实生活中分析变量之间关系的有力工具，适用于解决各领域的实际问题。然而，在现实生活中，问题的复杂性使得事件往往存在模糊性和不精确性，导致数据难以用简单的精确数表示。为此，许多研究人员通过模糊集理论来修改和扩展统计回归分析的相关模型，建立了模糊回归模型，并用于金融、生物等多个领域。

在模糊回归分析的应用实例中，研究者发现，数据离群点的出现会影响模型的拟合效果。以往的回归分析模型，往往使用最小二乘方法，该方法对于离群点的敏感性高，当含有个别偏差大的数据的时候，效果并不理想。相对于最小二乘方法，最小一乘回归对离群点具有更强鲁棒性。但最小一乘方法的目标函数存在不连续，难以求导等问题。因此，为其找到科学有效的求解方法十分重要。论文研究具有精确输入、模糊输出系统的建模及求解问题，建立了多种基于最小一乘的模糊回归模型，并给出其求解方法。选题具有理论和应用研究价值，内容上有一定的创新。论文主要工作包括：

1. 针对模糊输入，模糊输出系统的建模问题，建立了目标函数中带L₂正则项和L₁正则项的模糊最小一乘线性回归模型，设计了基于Split-Bregman方法的模型求解算法，并借助员工绩效评估问题的实验分析，验证了其部分模糊测度指标上优于以往的模糊线性回归模型。

2. 针对精确输入，模糊输出系统的建模问题，提出模糊最小一乘支持向量回归模型，给出模型求解算法，并将借助对系统评分预测问题实验分析，验证了其有效性和先进性。

Regression analysis is a powerful tool for analyzing the relationship between variables in real life and has broad applicability to solve practical problems in various fields. However, in real life, the complexity of problems makes events often ambiguous and imprecise, making it challenging to represent data with simple exact numbers. For this reason, many researchers have modified and extended the relevant models of statistical regression analysis using fuzzy set theory to establish fuzzy regression models, which have been used in various fields such as finance and biology.

In the application examples of fuzzy regression analysis, researchers have found that the presence of data outliers affects the model's fit. Previous regression analysis models, often using the least squares method, which is highly sensitive to outlier points, do not work well when containing data with large individual deviations. Compared with the least square method, the least absolute deviation method is more robust to outliers. However, the objective function of the absolute deviation method has problems such as discontinuity and difficulty in derivation. Therefore, it is important to find a scientific and effective solution to it. The paper investigates the modeling and solution problems of systems with exact inputs and fuzzy outputs, establishes a variety of fuzzy regression models based on the least absolute deviation method. and gives its solutions. The selected topic is of theoretical and applied research value, with some innovation in content. The main work of the paper includes.

1. For the modeling problem of a system with fuzzy inputs and fuzzy outputs, a fuzzy linear regression model with L₂ regular term and L₁ regular term in the objective function is established, a solution algorithm based on the Split-Bregman method is proposed, and its superiority over the previous fuzzy linear regression models is verified with the experimental analysis of the employee performance evaluation problem.

2. For the modeling problem of a system with exact inputs and fuzzy outputs, a model based on fuzzy least absolute deviation support vector regression is set up, the model-solving algorithm is given, and its usefulness and progress are tested with the experimental analysis of the system rating prediction problem.