管理工程学报2012，Vol.26Issue(4)：192-198,7.
基于梯形模糊数的分层多目标线性规划模型在多属性不确定决策问题中的应用
Hierarchical Multiple Objective Programming Model for Multiple Attribute Decision Making Problems Based on Trapezoidal Fuzzy Numbers
摘要
Abstract
In the face of multi-criteria decision making (MCDM) problem, decision makers are often facing the challenges of having limited knowledge, time pressure, and objective uncertainty. As a result, many existing models based on environment certainty cannot address practical problems. The purpose of this paper is to develop a hierarchical multi-objective linear programming model and solve multi-attribute decision making problems using trapezoidal fuzzy numbers. In this methodology, trapezoidal fuzzy numbers are constructed to capture the weights of attributes based on the preference information of decision makers. In the specific modeling process, according to the own characteristics of the trapezoidal fuzzy numbers, we establish four objective functions, and then solve this model with lexicographic optimization theory. In the first section, we discuss the features of trapezoidal fuzzy numbers, and define membership function, some algorithms, as well as the Euclidean distance formula based on trapezoidal fuzzy numbers. These detailed descriptions on the fundamental theories provide sufficient theoretical background information. In the second section, we establish the main models for multi-criteria decision making problems, and present step-by-step solutions. The lexicographic optimization method is introduced to solve this hierarchical multiple objective programming model and to determine the ideal solution and the attribute weights. The Hamming distance between trapezoidal fuzzy numbers is proposed, and the relative closeness of each alternative to the ideal solution is calculated with the principle of distance formula. The smaller the distance, the better solution can be achieved. Lastly, the ranking order of all evaluation alternatives is determined. In the end, we empirically make a comparable analysis between the proposed model based on trapezoidal fuzzy numbers and the existing model based on triangular fuzzy numbers. The empirical data, which are in the aspects of economic efficiency, resource conservation, environmental protection and social contribute, is obtained from several industrial enterprises in five different cities, including Shenzhen, Guangzhou, Wuhan, Zhuzhou and Hangzhou. In the data collection process, Delphi method and expert interviews are adopted. The result shows that the comprehensive rankings of these enterprises based on the abovementioned four aspects. Finally, our analyses show the advantages and disadvantages of trapezoidal fuzzy number and triangular fuzzy numbers and provide evidence on the practicality and feasibility of our models.关键词
分层多目标线性规划模型/多属性决策问题(MADM)/梯形模糊数Key words
hierarchical multi-objective linear programming model/ multiple attribute decision making (MADM) / trapezoidal fuzzy numbers分类
信息技术与安全科学引用本文复制引用
陈晓红,胡文华,曹裕,陈建二..基于梯形模糊数的分层多目标线性规划模型在多属性不确定决策问题中的应用[J].管理工程学报,2012,26(4):192-198,7.基金项目
国家自然科学基金创新群体科学基金资助项目(70921001),国家自然科学基金青年基金资助项目(71001108) （70921001）
