CAJ | 학술논문

文中首先建立了基于梯形模糊数的分层多目标线性规划模型,应用梯形模糊数来表示专家偏好信息。然后通过运用分层序列优化方法求解该模型,得出不同方案的模糊属性值和理想方案值,再根据模糊数的距离公式,求出每一个评价方案与理想方案之间的差值,然后得出评价方案之间的排序。最后,本文选择了深圳、广州、武汉、株洲、杭州五市的工业企业作为研究对象,分别用梯形模糊数和三角模糊数表示它们在经济效益、资源节约、环境保护和社会效益方面的综合情况,并根据本文所建立的模型和已有的基于三角模糊数的模型来进行比较分析,得出这些不同地区的企业在这四个方面的综合排名。通过这个实例的分析,也进一步证明和强调了文中所建立模型的实用性和可行性。
문중수선건립료기우제형모호수적분층다목표선성규화모형,응용제형모호수래표시전가편호신식。연후통과운용분층서렬우화방법구해해모형,득출불동방안적모호속성치화이상방안치,재근거모호수적거리공식,구출매일개평개방안여이상방안지간적차치,연후득출평개방안지간적배서。최후,본문선택료심수、엄주、무한、주주、항주오시적공업기업작위연구대상,분별용제형모호수화삼각모호수표시타문재경제효익、자원절약、배경보호화사회효익방면적종합정황,병근거본문소건립적모형화이유적기우삼각모호수적모형래진행비교분석,득출저사불동지구적기업재저사개방면적종합배명。통과저개실례적분석,야진일보증명화강조료문중소건립모형적실용성화가행성。
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 resuh, 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.