Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

Table 4

Scores and ranks of the 30 provinces of the 5 DEA models.

Province	CCR	Cross-efficiency methods			Proposed
		Benevolent	Aggressive	Neutral
Beijing	1.0000 1	0.9416 2	0.7782 3	0.9327 2	0.8874 3
Tianjin	0.8812 6	0.5220 12	0.4479 13	0.5261 12	0.4920 13
Hebei	0.3069 27	0.2814 25	0.2495 25	0.2794 25	0.2656 25
Shanxi	0.2826 29	0.2268 28	0.1883 28	0.2180 27	0.2022 27
Inner Mongolia	0.4851 22	0.3209 23	0.2529 24	0.2906 24	0.2756 24
Liaoning	0.5161 21	0.3615 22	0.3014 21	0.3542 21	0.3279 21
Jilin	0.3683 24	0.2996 24	0.2619 23	0.2965 23	0.2853 23
Heilongjiang	0.8715 7	0.7100 6	0.6060 6	0.7008 6	0.6705 6
Shanghai	0.6940 14	0.5823 9	0.4968 11	0.5880 9	0.5523 10
Jiangsu	1.0000 1	0.9727 1	0.8931 1	0.9697 1	0.9264 1
Zhejiang	1.0000 1	0.9344 3	0.8648 2	0.9175 3	0.8886 2
Anhui	1.0000 1	0.7753 4	0.7222 4	0.7805 4	0.7686 4
Fujian	0.7333 12	0.4688 15	0.3962 15	0.4403 16	0.4054 16
Jiangxi	0.4506 23	0.4109 19	0.3554 18	0.4072 19	0.3844 17
Shandong	0.8549 8	0.5422 10	0.5489 8	0.5666 10	0.5720 9
Henan	0.7968 11	0.4887 14	0.4813 12	0.4980 14	0.5096 12
Hubei	0.5486 20	0.4540 16	0.3871 16	0.4544 15	0.4309 15
Hunan	0.8088 10	0.5188 13	0.5135 10	0.5329 11	0.5404 11
Guangdong	1.0000 1	0.7737 5	0.7203 5	0.7688 5	0.7407 5
Guangxi	0.2911 28	0.2352 26	0.2232 26	0.2319 26	0.2285 26
Hainan	0.3165 26	0.1747 29	0.1283 29	0.1463 29	0.1295 29
Chongqing	0.6921 15	0.4354 18	0.3542 19	0.4100 18	0.3682 19
Sichuan	0.6977 13	0.6131 8	0.5539 7	0.6175 8	0.5899 8
Guizhou	0.6456 18	0.4534 17	0.3698 17	0.4192 17	0.3830 18
Yunnan	0.5494 19	0.4026 20	0.3217 20	0.3770 20	0.3491 20
Shanxi	0.8268 9	0.6435 7	0.5300 9	0.6463 7	0.6132 7
Gansu	0.6540 17	0.5332 11	0.4226 14	0.5093 13	0.4782 14
Qinghai	0.6727 16	0.3920 21	0.2994 22	0.3367 22	0.3208 22
Ningxia	0.2377 30	0.1548 30	0.1209 30	0.1390 30	0.1259 30
Xinjiang	0.3669 25	0.2335 27	0.1884 27	0.2160 28	0.1953 28