论文研究-基于指数型模糊数的多属性决策模型及其应用.pdf

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针对模糊多属性决策问题,给出一种基于指数型模糊数的多属性决策模型。一方面,通过定义指数型模糊数的期望,以实现属性权重向量的解模糊化处理;另一方面,根据三元区间数理论和指数型模糊数的截集信息,定义指数型模糊数上一种新的距离度量,以计算各备选方案与正、负理想方案之间的距离。根据模糊理想点思想,基于指数型模糊数的期望和距离的定义,给出一种指数型模糊数上的Topsis多属性决策方法。将该模型应用于一个具体实例,其结果证实了该方法的有效性。
l18 013,49(15) Computer Engineering and Applications计算机工程与应用 表1各属性指标值 x(0.89,0.03,0.06)(0.92,0.02,0.03)(0.95,0.05,0.02)00.93,0.02,0.02)00.92,0.02,0.04)(0.87,0.02,0.03) x2(0.91,0.030.04)(0.86.0.02,0.04)(0.94,0.03,0.03)(0.94,0.03,0.02)(0.89,0.03,0.03)0.92,0.01,0.02) X3(0.85,0.05.005)(0.92.0.02.0.03)0.94.0.03,0.01)(0.96.0.03,0.03)0.91,0.01,001)(0.97,0.02,002) X (0.95,0.05,0.0 (0.89,0.01,0.03)(0.92,002,0.03)(0.92,0.02,0.03)0.97,0.03,0.01)(0.93,0.03,0.02) X0.87,0.02,0.03)(0.93,0.02,0.02)(0.88,0.03,0.02)(0.89,0.03,0.04)(0.90,0.03,0.04)(0.93,0.01,003) 行解模糊化处理,即 且各属性值都以指数型模糊数形式绐出,如表1所示 D=cmy+4(O2y-)≤n (7) 已知属性权重向量 W=(0.20,0.02,0.03),(0.10,0.01,0.01) 并记W o. (0.25,0.03,0.02)(0.10,0.01,0.02) (2)进行归一化处理,即 (0.20,0.03.0.02).(0.15.0.01.0.03) 试对5个合作伙伴进行排序,并给出最优合作伙伴 (1≤j≤n) 基于指数型模糊数的 TOPSIS多属性决策方法,具体 实现如下 进而归一化属性权重向量W=(a1,2,…,n (1)根据表1构建决策矩阵R 89.0.03,0.06)(0.92,0.02,0.03)(0.95,0.05,0.02)(0.93.0.02,0.02)(0.92.0.02,0.04)(0.87,0.02,0.03) (0.91,0.03,0.04)(0.86,002,0.04)(094,0.03,0.03)(0.94,0.03,0.02)(0.89,0.03,03)(092,01,0.02 R=(0.85.0.05,0.05092.0.02,0.03)(094.0.093,0.01)0.96.0.03.0.03)091.0.01.0.01)0.97.0.02,0.02 (095,005,0.05)(089,0.01,0.03)(0.92,002,0.03)(0.92,002,03)(0.97,003,001)(0.93,003,0.02) (087.0.02,0.03)(093,0.02,0.02)(0.880.03,002)(0.89,003.0.04)0.90.0.03.0.04)093,0.01,0.03 步骤5利用距离公式(4),分别计算方案X与正、负 (2)囚各属性指标均为效益型,利用式(5)对模糊决策 理想方案之间的加权距离,即 知阵R进行规范化处理,得规范化模糊决策矩阵R′: 0.937.0.034.0.067)(0.989,0.040.0.060)(1.000.0.125,0.050)(0.969,0.030,0.030)(0.948.0.060,0.120)(0.897,0.060,0.090 (0.958,0.034,01045)(0.925,0.040,0.080)(0.989,0.075,0.075)(0.979,0.0450030)(0.918,0090.0.090)(0.948,0.030,0.060 R′=(0.895.0.033.0.044)(0.989,0.040,0.060)0.989,0.075,0025)(1.000,0.045.0.045)(0.938,0.030.0.030)(1.00.0.060.0.060) (1.000,0.056,0.056)(0.957,0.020,0.060)(0.968,0.050,0.075)(0.958,0.030,0.045)(1.000,0.090,0.030)(0.959,0.090.0.0601 (0.916.0.022,0.034)(1.000,0.040.0.040)(0.926,0.075,0.050)(0.927,0.045.0.060)(0.928.0.090.0.120)(0.959,0.030.0.090 D}=∑oDGn2X)(≤≤m) (9) (3)根据步骤3,确症正理想方案和负理想方案,得 x+-[.000,0.022,0.067)(1.000,0.020,0.080) ∑D(…X)(1≤i (10) (1.000,0.050.0.075).(1.000,0.030,0.060 (1.000.0.030,0.120)(1.000,0.030,0.090) 步骤6计算各个方案的相对贴近度 X=(0.895,0.056,0.034)(0.925,0.040,0.040) D (≤i≤m) (0.926,0.075,0.025)(0.927,0.045,0.030) D+D 0.918,0.090,0.030,(0.948,0.090.0.060)] 根据所有备选方案的相对贴近度进行排序,从而确定 (4)利用式(2),对属性权重向量W进行解模糊化处 最优方案。 理,得W=(0,204,0.100,0.246,0.104,0.196,0.159),进一步 得“归一化”权重向量:W′=(0.203,0.099,0.243.0.104,0.194 4应用实例 0.157) 某个业拟选择一个合作伙伴进行项目合作,共有5个 (5)计算各方案与正理想方案、负理想方案的加权距 潜在的合作伙伴(备选方案)X(=1,2,…,5)可供选样。离,见表2的第四、第五列。 每个方案对应6个属性指标(=1,2,…,6),均为效益型 (6)计算各方案的相对贴近度,见表2第六列 表2各方案与正、负理想方案的距离、加权距离、相对贴近度及排序 排序 k1[0,074,0029,0.0220058,0.079,0.30][0.071,0.082,0.0960.0550.1100.051100650.081 x2[0.062,0.093,0.033,0.048,0.135,0.079][0.0830035,0.1070.0520.053,0.053]00730.07004903 X;[0.135,0.029,0.0550.0130.142.0.027][0.020,0.082,0.063.0.0860.0730.079]0.0770.0630 [0.010,0.061,0.032,0.055,0053,0.094]0.125,0.0500.086,0.044,0.082,0.011]0.0470.0730.608 [0.I3,0.018,0.108.0.086,0.250.041]0.051,0.075,0.022.0.027.0.090,0.064]0.0910.0530.36 5 (下转132页

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