subjection理学硕士学位论文
张晓慧
哈尔滨工业大学
2004年7月
国内图书分类号：TP183
国际图书分类号：681.518.5
理学硕士学位论文
模糊数学在综合评价中的应用
硕 士 研究生：张晓慧
导 师：冯英浚 教授
申请学位级别：理学硕士
学 科、专 业：运筹学与控制论
所 在 单 位 ：数学系
答 辩 日 期 ：2004年7月
授予学位单位：哈尔滨工业大学
Classified Index: TP183
U.D.C: 681.518.5
Dissertation for the Master Degree in Science
THE APPLICATION OF FUZZY
MATHEMATIC IN POLY-INDEX
EV ALUATION
Candidate: Zhang Xiaohui
Supervisor: Prof. Feng Yingjun
Academic Degree Applied for:Master of Science
Speciality: Operational Research and Cybernetics Date of Oral Examination: July, 2004
University: Harbin Institute of Technology
哈尔滨工业大学理学硕士学位论文
摘要
评价已经深入到人们生活的各个方面，因此对评价方法的研究显得至关重要。我们认为评价是人的一种智能活动，由于被评对象往往受各种不确定性因素的影响，而模糊性又是其中最为主要的。因此将模糊数学这种人工智能的工具应用于评价就显得非常自然和必要。
测算决策单元同时面向输入和输出时的相对有效性的DEA模型。并且选择不同的隶属函数可使模型具有不同的侧重点，使模型能更好地反映评价的实际。
另一方面对传统的模糊综合评价模型进行改进，提出两种改进模型。一是改进了模糊矩阵合成算子，该算子具有非线性形式，它既能保留所有的评价信息，又可以弥补线性加权平均型算子存在的不足。二是将ULSI神经元模型融入到模糊综合评价中，提出基于ULSI神经元的模糊综合评价模型，该模型解决了在模糊综合评价中模糊矩阵合成算子的选取问题以及权重设定的主观性等问题，使得评价过程更为简单，评价结果更为客观。
关键词 模糊数学；数据包络分析；模糊综合评价；非线性；神经网络
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哈尔滨工业大学理学硕士学位论文
Abstract
Since the everyday life is full of evaluation, it is very important to search for its method. It is believed that evaluation is an intelligent activity, which is influenced by many uncertain factors, while the fussy factor is the primary one. So it is very natural and necessary to apply fuzzy mathematics to evaluation.
In this thesis, on the one hand, fuzzy mathematics is applied to data envelopment analysis (DEA), which is in common use in evaluation, to develop the general form of BCC model of DEA, which solves the limitation of the traditional DEA model that can only deal with one aspect, input or output, of the decision unit. The model can measure the relative efficiencies of decision units with the consideration of both input and output simultaneously. And in order to reflect the different emphases, different subjection functions can be chosen.
On the other hand, in order to improve the traditional fuzzy poly-index evaluation, two improved model of fuzzy evaluation are presented. One of these is presenting an improved fuzzy operator, which is nonlinear and it can not only save all the information in evaluation but also dispel the flaws of the linear weighted operator. The other of these is applying Utilization of Local Sample Information (ULSI) neutral unit to the fuzzy poly-index evaluation, which solve the two main problems in the fuzzy evaluation, which are the difficulties of the choice of the fuzzy operator and the fuzzy weight. The model makes the evaluation more convenient and more impersonal.
Keyword: fuzzy mathematics; data envelopment analysis; fuzzy poly-index evaluation; nonlinear; neutral network
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