多属性相似度一致性投影决策法

doi:10.12305/j.issn.1001-506X.2022.09.21

摘要/Abstract

摘要：

针对多属性决策与评价问题中投影法存在平面空间一系列评价失效情况, 提出了一种相似度一致性的投影决策法。首先, 给出了理想偏移向量的定义, 其中包含了理想决策的偏移程度和决策者的偏好; 其次, 根据理想偏移向量, 构造了一种新的综合评价函数; 然后, 按照投影决策法的基本步骤, 得到各方案的综合评价值。有效性分析表明, 新提的方法对模相似度、距离相似度、余弦相似度和方向相似度都有综合考量, 从而能避免单一相似度的不全面和综合评价函数的失效。最后, 通过案例分析验证了方法合理有效。

关键词: 多属性决策, 投影决策法, 相似度一致性, 偏好系数

Abstract:

Aiming at a series of evaluation failures in the plane space of the projection method in the multi-attribute decision-making and evaluation problem, a similarity consistency projection decision-making method is proposed. First, the definition of the ideal offset vector is given, which includes the offset degree of the ideal decision and the preference of the decision maker. Secondly, a new comprehensive evaluation function is constructed according to the ideal offset vector. Then the comprehensive evaluation value of each program is obtained according to the projection of the basic steps of the method. The effectiveness analysis shows that the newly proposed method has comprehensive considerations on modular similarity, distance similarity, cosine similarity and direction similarity, so as to avoid the incompleteness of single similarity and the failure of comprehensive evaluation function. Finally, a case study shows that the method is reasonable and effective.

Key words: multi-attribute decision-making, projection decision-making method, similarity consistency, preference coefficient

中图分类号:

C934

郑诺希, 李武, 周小强, 刘钢. 多属性相似度一致性投影决策法[J]. 系统工程与电子技术, 2022, 44(9): 2869-2877.

Nuoxi ZHENG, Wu LI, Xiaoqiang ZHOU, Gang LIU. Projection decision method for consistency of multiple attribute similarity[J]. Systems Engineering and Electronics, 2022, 44(9): 2869-2877.

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省/直辖市	G₁	G₂	G₃	G₄	G₅
北京(X₁)	47 177	16.61	8.89	31.05	15.77
天津(X₂)	43 323	9.08	3.65	29.8	8.44
上海(X₃)	59 023	13.84	6.06	26.55	12.87
江苏(X₄)	46 821	10.59	3.51	22.46	7.41
浙江(X₅)	41 646	13.24	4.64	24.33	9.33
安徽(X₆)	26 446	10.16	2.38	26.8	9.85
福建(X₇)	38 381	11.97	4.79	26.45	10.64
广东(X₈)	57 808	10.29	4.54	23.0	9.23
辽宁(X₉)	28 869	7.68	2.12	31.08	9.05
山东(X₁₀)	38 812	8.92	3.38	25.68	8.73
湖北(X₁₁)	30 721	10.87	4.15	30.36	11.44
湖南(X₁₂)	24 848	10.77	2.42	30.71	11.37
河南(X₁₃)	26 925	9.34	3.06	30.11	10.84
江西(X₁₄)	23 269	8.25	2.58	32.57	8.62
河北(X₁₅)	28 267	8.13	3.17	29.25	9.17
山西(X₁₆)	21 583	7.41	4.66	35.35	11.27

方案	G₁	G₂	G₃	G₄	G₅
Y₁	0.683 6	1.0	1.0	0.333 6	1.0
Y₂	0.580 7	0.181 5	0.226 0	0.430 6	0.123 2
Y₃	1.0	0.698 9	0.582 0	0.682 7	0.653 1
Y₄	0.674 1	0.345 7	0.205 3	1.0	0.0
Y₅	0.535 9	0.633 7	0.372 2	0.854 9	0.229 7
Y₆	0.129 9	0.298 9	0.038 4	0.663 3	0.291 9
Y₇	0.448 7	0.495 7	0.394 4	0.690 5	0.386 4
Y₈	0.967 5	0.313 0	0.357 5	0.958 1	0.217 7
Y₉	0.194 6	0.029 3	0.0	0.331 3	0.196 2
Y₁₀	0.460 2	0.164 1	0.186 1	0.750 2	0.157 9
Y₁₁	0.244 1	0.376 1	0.299 9	0.387 1	0.482 1
Y₁₂	0.087 2	0.365 2	0.044 3	0.360 0	0.473 7
Y₁₃	0.142 7	0.209 8	0.138 8	0.406 5	0.410 3
Y₁₄	0.045 0	0.091 3	0.067 9	0.215 7	0.144 7
Y₁₅	0.178 5	0.078 3	0.155 1	0.473 2	0.210 5
Y₁₆	0.0	0.0	0.375 2	0.0	0.461 7

方案	G₁	G₂	G₃	G₄	G₅
A₁	0.157 0	0.187 6	0.155 7	0.088 6	0.161 4
A₂	0.133 3	0.034 0	0.035 2	0.114 4	0.019 9
A₃	0.229 6	0.131 1	0.090 6	0.181 3	0.105 4
A₄	0.154 8	0.064 9	0.032 0	0.265 6	0
A₅	0.123 0	0.118 9	0.058 0	0.227 1	0.037 1
A₆	0.029 8	0.056 1	0.006 0	0.176 2	0.047 1
A₇	0.103 0	0.093 0	0.061 4	0.183 4	0.062 4
A₈	0.222 1	0.058 7	0.055 7	0.254 5	0.035 1
A₉	0.044 7	0.005 5	0	0.088 0	0.031 7
A₁₀	0.105 7	0.030 8	0.029 0	0.199 3	0.025 5
A₁₁	0.056 0	0.070 6	0.046 7	0.102 8	0.077 8
A₁₂	0.020 0	0.068 5	0.006 9	0.095 6	0.076 5
A₁₃	0.032 8	0.039 4	0.021 6	0.108 0	0.066 2
A₁₄	0.010 3	0.017 1	0.010 6	0.057 3	0.023 4
A₁₅	0.041 0	0.014 7	0.024 1	0.125 7	0.034 0
A₁₆	0	0	0.058 4	0	0.074 5

方案	评价值	方案	评价值	方案	评价值
A₁	0.310 0	A₇	0.238 2	A₁₃	0.124 9
A₂	0.164 1	A₈	0.305 1	A₁₄	0.057 0
A₃	0.340 6	A₉	0.085 9	A₁₅	0.118 0
A₄	0.258 3	A₁₀	0.195 1	A₁₆	0.043 7
A₅	0.271 4	A₁₁	0.159 8
A₆	0.154 3	A₁₂	0.121 2

方案	α_i	\|\|d_i\|\|	r_i	T_{β_i}=0	T_{β_i}=1
A₁	0.751 8(3)	0.191 3(2)	0.924 4(5)	0.343 5(3)	0.317 5(2)
A₂	0.401 5(9)	0.300 5(9)	0.907 6(7)	0.183 4(9)	0.166 5(8)
A₃	0.764 8(1)	0.132 9(1)	0.980 8(1)	0.349 4(1)	0.342 7(1)
A₄	0.691 2(4)	0.249 0(6)	0.854 1(13)	0.315 8(4)	0.269 7(5)
A₅	0.640 3(5)	0.206 3(3)	0.941 8(4)	0.292 5(5)	0.275 5(4)
A₆	0.422 9(8)	0.317 3(10)	0.823 5(15)	0.193 2(8)	0.159 1(10)
A₇	0.538 6(6)	0.224 6(5)	0.973 4(3)	0.246 1(6)	0.239 5(6)
A₈	0.764 1(2)	0.206 8(4)	0.902 4(8)	0.349 1(2)	0.315 0(3)
A₉	0.227 2(14)	0.374 1(14)	0.838 8(14)	0.103 8(14)	0.087 1(14)
A₁₀	0.505 5(7)	0.280 8(7)	0.868 3(10)	0.230 9(7)	0.200 5(7)
A₁₁	0.359 1(10)	0.298 7(8)	0.976 9(2)	0.164 1(10)	0.160 3(9)
A₁₂	0.310 5(11)	0.341 1(12)	0.867 8(11)	0.141 9(11)	0.123 1(12)
A₁₃	0.302 8(13)	0.335 5(11)	0.912 1(6)	0.138 4(13)	0.126 2(11)
A₁₄	0.144 2(16)	0.400 8(15)	0.870 9(9)	0.065 9(16)	0.057 4(15)
A₁₅	0.305 1(12)	0.344 4(13)	0.860 3(12)	0.139 4(12)	0.119 9(13)
A₁₆	0.207 2(15)	0.418 9(16)	0.488 3(16)	0.094 7(15)	0.046 2(16)