南通大学学报（自然科学版）

为了进一步完善路面养护“四新”技术后评价体系，本文采用融入决策者偏好因素的指标权重向量法，提出一种基于松弛变量与扩展拉格朗日乘数的改进模糊聚类算法。通过引入松弛变量，将体现决策者偏好的不等式约束转化为等式约束，构建了新的优化目标函数。在此基础上，推导出偏好设定下权重矢量的显式解析表达式，建立了完整的理论求解框架，得出在给定偏好条件下权重向量的精确解析表达式。最后，将该模型应用于“四新”技术的实际项目中，得到各指标在以路面性能为偏好的约束条件下所得的权重：材料性能w₁=0.072 0，路面状况w₂=0.204 9，使用寿命w₃=0.144 8，适配程度w₄=0.164 9，管理者费用w₅=0.188 8，使用者费用w₆=0.045 4，碳排放w₇=0.179 2。通过对比本文方法与其他方法，进一步验证了所提模型的合理性和有效性。

In order to further improve the post evaluation system of the “Four New″ technologies(new materials, new technologies, new processes, and new equipment) for road maintenance, the study adopts an index weight vector method that incorporates decision-makers′ preference factors, and proposes an improved fuzzy clustering algorithm based on slack variables and extended Lagrange multipliers. By introducing slack variables, the equality constraints reflecting the decision maker′s preference are transformed into equality constraints, and a new optimization objective function is constructed. On this basis, the explicit analytic expressions of the weight vectors under the preference setting are derived, and a complete theoretical solution framework is established to derive the exact analytic expressions of the weight vectors under the given preference conditions. Finally, the model is applied to the actual project of the “Four New″ technologies, and the weights of each index are obtained under the constraints of the preference of pavement performance: material performance w₁= 0.072 0, pavement condition w₂= 0.204 9, service life w₃= 0.144 8,degree of adaptation w₄= 0.164 9, managerial costs w₅= 0.188 8, user costs w₆= 0.045 4, carbon emission w₇=0.179 2. Comparing this method with other methods further validates the rationality and effectiveness of the paper′s model.