| 表1. 属性的权重
Tab.1Weights of Attributes
 |
 |
 |
[ ] |
[ ] |
 |
| [0.3350， 0.3755] |
[0.3009， 0.3138] |
[0.3194， 0.3363] |
表2.方案的属性权重
Tab.2 The Attribute Weights of Alternatives
 |
|
|
|
 |
[0.214， 0.220] |
[0.166， 0.178] |
[0.184， 0.190] |
 |
[0.206， 0.225] |
[0.220， 0.229] |
[0.182， 0.191] |
 |
[0.195， 0.204] |
[0.192， 0.198] |
[0.220， 0.231] |
 |
[0.181， 0.190] |
[0.195， 0.205] |
[0.185， 0.195] |
 |
[0.175， 0.184] |
[0.193， 0.201] |
[0.201， 0.211] |
表 3. Bryson 与 Mobolurin方法的计算结果 [9]
Tab.3 The Calculation Results of Bryson and Mobolurin’sapproach [9]
| 方案 |
Medians of the 'level 3 composite' intervals |
'level 3 composite' intervals |
Crisp values (level 1) |
|
0.1933 |
[0.1890，0.1976] |
0.1951 |
|
0.2088 |
[0.2022， 0.2154] |
0.2092 |
|
0.2067 |
[0.2021， 0.2112] |
0.2076 |
|
0.1914 |
[0.1865， 0.1964] |
0.1909 |
|
0.1936 |
[0.1888， 0.1983] |
0.1972 |
| Ranking by crisp values (level 1) |
>>>> |
| |
|
|
|
|
基于公式(13)，决策矩阵被转换化为：
这样，可以建立下面的线性规划模型：
 (16a)
s.t.
 (16b)
 (16c)
 (16d)
 (16e)
模型(16)的最优解为w=(0.3668，0.3138，0.3194)。因此，5个大学教员的综合评价值分别为 =0.3467， =0.6364， =0.3535， =0.2554， =0.3115，进而得到他们的排序>>>>。
5.结论
针对人员评价多属性决策问题，本文提出了一个新的、简单的方法。这个方法由3个部分组成：(1).通过计算各属性值与负理想属性值的相对距离将区间数决策矩阵转换为单点值矩阵；(2).基于单点值决策矩阵，建立线性规划模型来求解属性的权重值以使得每个决策方案的综合评价值最大化；(3).基于简单加权法[1]，采用计算得到的属性权重值计算方案的综合评价值并给出它们的排序。本文提出的方法具有创新性并克服了由Bryson和Mobolurin(1996)所提出方法的缺点[9]：方案的综合评价值的计算基于相同的属性权重值。相对于由Bryson和Mobolurin(1996)所提出方法，本文提出的方法具有计算简单、易于操作的特点，而且很容易地实现为计算机信息系统。因此，本文提出的方法具有广泛的应用性。
参考文献 (References)
[1] Hwang C.L. and Yoon K. Multiple Attribute Decision Making: Methodsand Applications [M]. New York: Springer-Verlag, 1981.
[2] Saaty T.L. The Analytic HierarchyProcess [M]. New York: McGraw-Hill, 1980.
[3] Saaty T.L. and Vargas L.G. Uncertainty and rank order in the AnalyticHierarchy Process [J]. European Journal of Operational Research, 1987, 32: 107-117.
[4] Arbel A. Approximate articulation of preference andpriority derivation [J]. European Journal of Operational Research, 1989, 43: 317-326.
[5] Boender C.G.E., Graan J.G. and Lootsma F.A. Multi-criteria decision analysis with fuzzypairwise comparison [J]. Fuzzy Sets and Systems, 1989, 29: 133-143.
[6] Arbel A. and Vargas L.G. Preference simulation and preference programming: robustness issues inpriority derivation [J]. European Journal of Operational Research, 1993, 69: 200-209.
[7] Haines L.M. A statistical approachto the analytic hierarchy process with interval judgements. (I). Distributions on feasible regions [J]. EuropeanJournal of Operational Research, 1998, 110: 112-125.
[8] Yoon K.P. The propagation of errorsin multiple-attribute decision analysis: a practical approach [J]. Journal of the Operational Research Society, 1989, 40 (7):681-686.
[9] Bryson N. and Mobolurin A. Anaction learning evaluation procedure for multiple criteria decision makingproblems [J]. European Journal of Operational Research, 1996, 96(2):379-386.
[10] Raj P.A. and Kumar, D.N. Ranking alternativeswith fuzzy weights using maximizing set and minimizing set [J]. Fuzzy Sets and Systems, 1999, 105: 365-375.
[11] Cheng C.H. Evaluating weaponsystems using ranking fuzzy numbers [J]. Fuzzy Sets andSystems, 1999, 107: 25-35.
[12] Kreyszig E. Advanced Engineering Mathematics [M]. New York: Wiley, 1999.
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