Some series of intuitionistic fuzzy interactive averaging aggregation operators

Garg, Harish

doi:10.1186/s40064-016-2591-9

SpringerPlus

Table 2 Ordering of the alternatives for different \(\gamma\)

From: Some series of intuitionistic fuzzy interactive averaging aggregation operators

\(\gamma\)	Approach	Score function by IFHIWA				Score function by IFHIOWA				Score function by IFHIHWA
\(\gamma\)	Approach	\(S(x_1)\)	\(S(x_2)\)	\(S(x_3)\)	Ranking	\(S(x_1)\)	\(S(x_2)\)	\(S(x_3)\)	Ranking	\(S(x_1)\)	\(S(x_2)\)	\(S(x_3)\)	Ranking
0.1	Proposed	0.1386	0.1298	0.0060	\(x_1 \succ x_2 \succ x_3\)	0.1386	0.1298	0.0060	\(x_1 \succ x_2 \succ x_3\)	0.1790	0.1260	0.0294	\(x_1 \succ x_2 \succ x_3\)
0.1	Liu (2014)	0.1984	0.1878	0.0464	\(x_1\succ x_2\succ x_3\)	0.1984	0.1878	0.0464	\(x_1\succ x_2\succ x_3\)	0.2280	0.2227	0.0811	\(x_1\succ x_2\succ x_3\)
0.5	Proposed	0.1214	0.1183	−0.0039	\(x_1 \succ x_2 \succ x_3\)	0.1214	0.1183	−0.0039	\(x_1 \succ x_2 \succ x_3\)	0.1625	0.1107	0.0211	\(x_1 \succ x_2 \succ x_3\)
0.5	Liu (2014)	0.1722	0.1627	0.0288	\(x_1\succ x_2\succ x_3\)	0.1722	0.1627	0.0288	\(x_1\succ x_2\succ x_3\)	0.2105	0.2072	0.0746	\(x_1\succ x_2\succ x_3\)
1.0	Proposed	0.1099	0.1099	−0.0114	\(x_2 \succ x_1 \succ x_3\)	0.1099	0.1099	−0.0114	\(x_2 \succ x_1 \succ x_3\)	0.1530	0.0996	0.0157	\(x_1 \succ x_2 \succ x_3\)
1.0	Liu (2014)	0.1588	0.1498	0.0178	\(x_1\succ x_2\succ x_3\)	0.1588	0.1498	0.0178	\(x_1\succ x_2\succ x_3\)	0.2023	0.2007	0.0721	\(x_1\succ x_2\succ x_3\)
1.5	Proposed	0.1029	0.1045	−0.0163	\(x_2 \succ x_1 \succ x_3\)	0.1029	0.1045	−0.0163	\(x_2 \succ x_1 \succ x_3\)	0.1479	0.0925	0.0127	\(x_1 \succ x_2 \succ x_3\)
1.5	Liu (2014)	0.1514	0.1425	0.0112	\(x_1\succ x_2\succ x_3\)	0.1514	0.1425	0.0112	\(x_1\succ x_2\succ x_3\)	0.1982	0.1978	0.0715	\(x_1\succ x_2\succ x_3\)
2.0	Proposed	0.0981	0.1007	−0.0199	\(x_2 \succ x_1 \succ x_3\)	0.0981	0.1007	−0.0199	\(x_2 \succ x_1 \succ x_3\)	0.1443	0.0876	0.0108	\(x_1 \succ x_2 \succ x_3\)
2.0	Liu (2014)	0.1467	0.1377	0.0068	\(x_1\succ x_2\succ x_3\)	0.1467	0.1377	0.0068	\(x_1\succ x_2\succ x_3\)	0.1960	0.1964	0.0716	\(x_1\succ x_2\succ x_3\)
3.0	Proposed	0.0918	0.0957	−0.0247	\(x_2 \succ x_1 \succ x_3\)	0.0918	0.0957	−0.0247	\(x_2 \succ x_1 \succ x_3\)	0.1400	0.0810	0.0087	\(x_1 \succ x_2 \succ x_3\)
3.0	Liu (2014)	0.1408	0.1316	0.0011	\(x_1\succ x_2\succ x_3\)	0.1408	0.1316	0.0011	\(x_1\succ x_2\succ x_3\)	0.1937	0.1941	0.0725	\(x_1\succ x_2\succ x_3\)
5.0	Proposed	0.0851	0.0902	−0.0300	\(x_2 \succ x_1 \succ x_3\)	0.0851	0.0902	−0.0300	\(x_2 \succ x_1 \succ x_3\)	0.1362	0.0738	0.0073	\(x_1 \succ x_2 \succ x_3\)
5.0	Liu (2014)	0.1349	0.1253	−0.0049	\(x_1\succ x_2\succ x_3\)	0.1349	0.1253	−0.0049	\(x_1\succ x_2\succ x_3\)	0.1926	0.1923	0.0753	\(x_1\succ x_2\succ x_3\)
10	Proposed	0.0785	0.0847	−0.0354	\(x_2 \succ x_1 \succ x_3\)	0.0785	0.0847	−0.0354	\(x_2 \succ x_1 \succ x_3\)	0.1337	0.0663	0.0074	\(x_1 \succ x_2 \succ x_3\)
10	Liu (2014)	0.1293	0.1192	−0.0107	\(x_1\succ x_2\succ x_3\)	0.1293	0.1192	−0.0107	\(x_1\succ x_2\succ x_3\)	0.1941	0.1925	0.0783	\(x_1\succ x_2\succ x_3\)
25	Proposed	0.0736	0.0804	−0.0396	\(x_2 \succ x_1 \succ x_3\)	0.0736	0.0804	−0.0396	\(x_2 \succ x_1 \succ x_3\)	0.1340	0.0596	0.0105	\(x_1 \succ x_2 \succ x_3\)
25	Liu (2014)	0.1252	0.1147	−0.0151	\(x_1\succ x_2\succ x_3\)	0.1252	0.1147	−0.0151	\(x_1\succ x_2\succ x_3\)	0.2006	0.1962	0.0803	\(x_1\succ x_2\succ x_3\)
50	Proposed	0.0717	0.0788	−0.0412	\(x_2 \succ x_1 \succ x_3\)	0.0717	0.0788	−0.0412	\(x_2 \succ x_1 \succ x_3\)	0.1355	0.0563	0.0108	\(x_1 \succ x_2 \succ x_3\)
50	Liu (2014)	0.1237	0.1130	−0.0167	\(x_1\succ x_2\succ x_3\)	0.1237	0.1130	−0.0167	\(x_1\succ x_2\succ x_3\)	0.2074	0.1918	0.0761	\(x_1\succ x_2\succ x_3\)
100	Proposed	0.0707	0.0779	−0.0421	\(x_2 \succ x_1 \succ x_3\)	0.0707	0.0779	−0.0421	\(x_2 \succ x_1 \succ x_3\)	0.1369	0.0535	0.0112	\(x_1 \succ x_2 \succ x_3\)
100	Liu (2014)	0.1229	0.1122	−0.0175	\(x_1\succ x_2\succ x_3\)	0.1229	0.1122	−0.0175	\(x_1\succ x_2\succ x_3\)	0.2052	0.1888	0.0731	\(x_1\succ x_2\succ x_3\)

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