考虑决策者偏好的洪水灾害模糊聚类迭代评估模型

决策者偏好对洪水灾害的评估结果有重要影响.传统的评估方法可能会出现次要指标权重过大的情况,难以有效体现决策者偏好对评估结果的影响,为此将模糊聚类迭代模型推广到考虑决策者偏好的情况,并给出单一偏好条件下的理论解,提出了基于决策者偏好模糊聚类迭代模型.在该模型中,通过增加一个松弛因子构造一个增广拉格朗日乘子添加到模糊聚类迭代模型的目标函数中,将体现决策者偏好的不等式约束转化为等式约束,并依此求出该偏好条件下权重向量的解析解,可为考虑决策者偏好评估方法的研究提供理论依据;再根据样本特征值矩阵与解得的最优权重向量求出各样本的灾情综合评价值,结合最优隶属度矩阵确定各样本所属洪灾等级,各等级内部样本依据灾情综合评价值排序.该模型直接利用样本特征值矩阵对洪灾样本灾情大小进行识别,降低对最优隶属度矩阵的依赖性,使得排序结果更准确合理.最后,将该模型应用于2013年四川省部分地区洪水资料,验证了考虑决策者偏好模糊聚类迭代模型的理论结果,灾情综合评价值法的排序结果比传统的类别特征值法更合理.

Flood disaster fuzzy clustering iterative assessment model considering preference information of decision-makers

Decision maker's preference has an important impact on the outcome of the flood disaster assessment. Traditional assessment methods may appear secondary index weight is too large. It is difficult to effectively reflect decision maker's preference on the evaluation result. Hence, the fuzzy clustering iterative (FCI) model is extended to consider the preference of decision-makers, then the theoretical solution under a single preference condition has been given, and the fuzzy clustering iterative model considering preference information of Decision-makers is presented. By means of adding a relaxation factor to construct an augmented Lagrange multiplier into the objective function of FCI model, the inequality constraints that embody the decision maker's preference can be translated into the equality constraints, then the analytic solution in this preference condition can be obtained, and proposes the theory solution for studies of evaluation methods considering the decision maker's preference. Then, the comprehensive evaluation index of each sample can be obtained according to the characteristic value matrix of the floods sample and the solved optimal weight. The levels of each sample are determined combined with optimal subordinate degree matrix, and the ranking in each level is achieved in accordance with the comprehensive evaluation index. The model uses the characteristic value matrix of the floods sample directly to identify the extent of disaster effects, and reduces the dependency on the optimal subordinate degree matrix, thus it gives a more accurate and reasonable ranking result. Finally, the proposed model is applied to analyze the flood data of Sichuan province in 2013, the result verifies that it can help us achieve a outcome of the flood disasters assessment that consider decision maker's preferences and it gives more reasonable ranking result than the traditional classificatory eigenvalue method.