多属性相似度一致性投影决策法

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

Abstract

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

CLC Number:

C934

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.

Figures/Tables 12

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Fig.3

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Fig.5

Table 1

Table 2

Table 3

Table 4

Fig.6

Table 5

Table 6

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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)

Projection decision method for consistency of multiple attribute similarity

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方法	排序	最优解
文献[4]	A₃>A₁>A₈>A₅>A₄>A₇>A₁₀>A₂> A₁₁>A₆>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃
文献[36]	A₃>A₁>A₈>A₅>A₇>A₄>A₁₀>A₂> A₁₁>A₆>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃
文献[40]	A₃>A₁>A₈>A₅>A₄>A₇>A₁₀>A₂> A₆>A₁₁>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃
文献[37]	A₃>A₁>A₅>A₈>A₇>A₄>A₁₁>A₁₀> A₂>A₁₃>A₆>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃
正交投影法^[35]	A₃>A₁>A₈>A₅>A₄>A₇>A₁₀>A₂> A₁₁>A₆>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃
双向投影法^[38]	A₈>A₁>A₃>A₄>A₅>A₇>A₁₀>A₂> A₆>A₁₁>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₈
本文方法	A₃>A₁>A₈>A₅>A₄>A₇>A₁₀>A₂> A₁₁>A₆>A₁₃>A₁₂>A₁₅>A₉>A₁₄>A₁₆	A₃

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