Single-valued neutrosophic TODIM method based on cumulative prospect theory for multi-attribute group decision making and its application to medical emergency management evaluation

Figures & data

Table 1. Decision matrix $U^{(1)}$ given by the expert $D_1.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.70,0.25,0.30〉$	$〈0.15,0.65,0.85〉$	$〈0.25,0.65,0.70〉$
$J_2$	$〈0.65,0.30,0.35〉$	$〈0.55,0.45,0.50〉$	$〈0.75,0.20,0.15〉$
$J_3$	$〈0.60,0.45,0.40〉$	$〈0.60,0.40,0.45〉$	$〈0.70,0.25,0.30〉$
$J_4$	$〈0.45,0.40,0.55〉$	$〈0.35,0.65,0.70〉$	$〈0.55,0.60,0.65〉$
$J_5$	$〈0.55,0.60,0.40〉$	$〈0.40,0.55,0.65〉$	$〈0.60,0.50,0.45〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.65,0.45,0.50〉$	$〈0.65,0.50,0.45〉$	$〈0.70,0.25,0.35〉$
$J_2$	$〈0.65,0.40,0.50〉$	$〈0.60,0.55,0.50〉$	$〈0.65,0.40,0.35〉$
$J_3$	$〈0.60,0.50,0.55〉$	$〈0.70,0.30,0.35〉$	$〈0.60,0.55,0.45〉$
$J_4$	$〈0.45,0.65,0.60〉$	$〈0.65,0.50,0.45〉$	$〈0.35,0.60,0.65〉$
$J_5$	$〈0.70,0.30,0.35〉$	$〈0.45,0.65,0.60〉$	$〈0.55,0.45,0.40〉$

Source: Ours.

Table 2. Decision matrix $U^{(2)}$ given by the expert $D_2.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.65,0.35,0.40〉$	$〈0.35,0.65,0.70〉$	$〈0.35,0.55,0.65〉$
$J_2$	$〈0.70,0.25,0.20〉$	$〈0.65,0.40,0.35〉$	$〈0.80,0.10,0.15〉$
$J_3$	$〈0.65,0.30,0.35〉$	$〈0.50,0.55,0.45〉$	$〈0.70,0.25,0.30〉$
$J_4$	$〈0.50,0.45,0.45〉$	$〈0.40,0.65,0.60〉$	$〈0.60,0.35,0.40〉$
$J_5$	$〈0.60,0.50,0.45〉$	$〈0.35,0.70,0.60〉$	$〈0.55,0.45,0.65〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.60,0.45,0.50〉$	$〈0.55,0.40,0.45〉$	$〈0.70,0.25,0.35〉$
$J_2$	$〈0.60,0.45,0.50〉$	$〈0.70,0.25,0.35〉$	$〈0.65,0.40,0.35〉$
$J_3$	$〈0.45,0.65,0.60〉$	$〈0.65,0.50,0.45〉$	$〈0.60,0.45,0.40〉$
$J_4$	$〈0.50,0.55,0.60〉$	$〈0.60,0.55,0.50〉$	$〈0.45,0.55,0.50〉$
$J_5$	$〈0.75,0.20,0.25〉$	$〈0.50,0.45,0.65〉$	$〈0.50,0.55,0.60〉$

Source: Ours.

Table 3. Decision matrix $U^{(3)}$ given by the expert $D_3.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.55,0.60,0.40〉$	$〈0.20,0.60,0.80〉$	$〈0.30,0.65,0.75〉$
$J_2$	$〈0.65,0.30,0.35〉$	$〈0.65,0.40,0.35〉$	$〈0.60,0.45,0.50〉$
$J_3$	$〈0.75,0.20,0.20〉$	$〈0.60,0.35,0.40〉$	$〈0.65,0.35,0.45〉$
$J_4$	$〈0.35,0.65,0.60〉$	$〈0.35,0.65,0.70〉$	$〈0.55,0.50,0.65〉$
$J_5$	$〈0.50,0.45,0.45〉$	$〈0.30,0.70,0.65〉$	$〈0.45,0.65,0.50〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.50,0.60,0.65〉$	$〈0.60,0.55,0.50〉$	$〈0.75,0.20,0.30〉$
$J_2$	$〈0.65,0.35,0.45〉$	$〈0.65,0.50,0.45〉$	$〈0.70,0.25,0.35〉$
$J_3$	$〈0.65,0.35,0.45〉$	$〈0.60,0.55,0.50〉$	$〈0.65,0.40,0.35〉$
$J_4$	$〈0.55,0.45,0.65〉$	$〈0.45,0.65,0.60〉$	$〈0.40,0.60,0.55〉$
$J_5$	$〈0.40,0.55,0.65〉$	$〈0.35,0.65,0.70〉$	$〈0.55,0.45,0.40〉$

Source: Ours.

Table 4. Decision matrix $U^{(4)}$ given by the expert $D_4.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.65,0.35,0.40〉$	$〈0.25,0.60,0.75〉$	$〈0.40,0.55,0.65〉$
$J_2$	$〈0.80,0.10,0.15〉$	$〈0.70,0.20,0.25〉$	$〈0.75,0.20,0.15〉$
$J_3$	$〈0.65,0.25,0.35〉$	$〈0.75,0.20,0.20〉$	$〈0.65,0.35,0.40〉$
$J_4$	$〈0.70,0.20,0.30〉$	$〈0.45,0.50,0.55〉$	$〈0.45,0.55,0.60〉$
$J_5$	$〈0.60,0.40,0.50〉$	$〈0.40,0.55,0.65〉$	$〈0.35,0.65,0.70〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.60,0.45,0.55〉$	$〈0.50,0.55,0.60〉$	$〈0.70,0.25,0.35〉$
$J_2$	$〈0.50,0.65,0.60〉$	$〈0.80,0.15,0.20〉$	$〈0.60,0.50,0.45〉$
$J_3$	$〈0.65,0.35,0.45〉$	$〈0.70,0.25,0.35〉$	$〈0.65,0.45,0.40〉$
$J_4$	$〈0.65,0.40,0.50〉$	$〈0.65,0.45,0.50〉$	$〈0.50,0.55,0.60〉$
$J_5$	$〈0.70,0.25,0.35〉$	$〈0.50,0.55,0.60〉$	$〈0.45,0.55,0.50〉$

Source: Ours.

Table 5. Decision matrix $U^{(5)}$ given by the expert $D_5.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.55,0.35,0.50〉$	$〈0.35,0.70,0.60〉$	$〈0.45,0.65,0.50〉$
$J_2$	$〈0.75,0.15,0.20〉$	$〈0.70,0.20,0.25〉$	$〈0.70,0.25,0.30〉$
$J_3$	$〈0.60,0.40,0.50〉$	$〈0.60,0.35,0.40〉$	$〈0.65,0.45,0.35〉$
$J_4$	$〈0.65,0.25,0.35〉$	$〈0.25,0.60,0.75〉$	$〈0.50,0.70,0.65〉$
$J_5$	$〈0.55,0.50,0.60〉$	$〈0.20,0.65,0.75〉$	$〈0.40,0.60,0.65〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.65,0.35,0.45〉$	$〈0.70,0.35,0.25〉$	$〈0.65,0.40,0.35〉$
$J_2$	$〈0.65,0.45,0.35〉$	$〈0.75,0.30,0.25〉$	$〈0.55,0.45,0.50〉$
$J_3$	$〈0.70,0.25,0.35〉$	$〈0.65,0.40,0.35〉$	$〈0.45,0.55,0.50〉$
$J_4$	$〈0.55,0.45,0.65〉$	$〈0.50,0.55,0.60〉$	$〈0.60,0.50,0.45〉$
$J_5$	$〈0.80,0.10,0.15〉$	$〈0.60,0.50,0.45〉$	$〈0.50,0.55,0.60〉$

Source: Ours.

Table 6. Group decision matrix $\tilde{Q}.$

	$F_1$	$F_2$	$F_3$
$J_1$	$〈0.6230,0.3642,0.4001〉$	$〈0.2701,0.6394,0.7278〉$	$〈0.3613,0.6049,0.6375〉$
$J_2$	$〈0.7229,0.1929,0.2277〉$	$〈0.6592,0.2987,0.3196〉$	$〈0.7292,0.2116,0.2170〉$
$J_3$	$〈0.6530,0.3052,0.3502〉$	$〈0.6246,0.3446,0.3562〉$	$〈0.6694,0.3266,0.3567〉$
$J_4$	$〈0.5621,0.3436,0.4227〉$	$〈0.3647,0.6013,0.6519〉$	$〈0.5289,0.5286,0.5791〉$
$J_5$	$〈0.5640,0.4807,0.4814〉$	$〈0.3322,0.5971,0.6601〉$	$〈0.4698,0.5675,0.5925〉$
	$F_4$	$F_5$	$F_6$
$J_1$	$〈0.6047,0.4484,0.5235〉$	$〈0.6044,0.4597,0.4306〉$	$〈0.6997,0.2663,0.3404〉$
$J_2$	$〈0.6098,0.4588,0.4730〉$	$〈0.7165,0.2997,0.3177〉$	$〈0.6290,0.3971,0.4011〉$
$J_3$	$〈0.6212,0.3909,0.4667〉$	$〈0.6629,0.3786,0.3924〉$	$〈0.5938,0.4764,0.4184〉$
$J_4$	$〈0.5512,0.4853,0.5941〉$	$〈0.5782,0.5325,0.5283〉$	$〈0.4757,0.5552,0.5419〉$
$J_5$	$〈0.7003,0.2323,0.3036〉$	$〈0.4928,0.5486,0.5884〉$	$〈0.5074,0.5127,0.4992〉$

Source: Ours.

Table 7. The modified weights ${\delta }_{1wh}^{\ast }(o_h).$

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
${\delta }_{12}^{*}$	0.9776	1.0000	0.9497	0.6998	0.6819	0.6785
${\delta }_{13}^{*}$	0.9776	1.0000	0.9497	0.6998	0.6819	0.6785
${\delta }_{14}^{*}$	0.9823	1.0000	0.9497	0.7479	0.7323	0.6785
${\delta }_{15}^{*}$	0.9823	1.0000	0.9497	0.6998	0.7323	0.6785

Source: Ours.

Table 8. The modified weights ${\delta }_{2wh}^{\ast }(o_h).$

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
${\delta }_{21}^{*}$	0.9816	1.0000	0.9586	0.7474	0.7318	0.6206
${\delta }_{23}^{*}$	0.9816	1.0000	0.9586	0.6993	0.7318	0.6781
${\delta }_{24}^{*}$	0.9816	1.0000	0.9586	0.7474	0.7318	0.6781
${\delta }_{25}^{*}$	0.9816	1.0000	0.9586	0.6993	0.7318	0.6781

Source: Ours.

Table 9. The modified weights ${\delta }_{3wh}^{\ast }(o_h).$

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
${\delta }_{31}^{*}$	0.9816	1.0000	0.9586	0.7474	0.7318	0.6206
${\delta }_{32}^{*}$	0.9776	1.0000	0.9497	0.7479	0.6819	0.6211
${\delta }_{34}^{*}$	0.9816	1.0000	0.9586	0.7474	0.7318	0.6781
${\delta }_{35}^{*}$	0.9816	1.0000	0.9586	0.6993	0.7318	0.6781

Source: Ours.

Table 10. The modified weights ${\delta }_{4wh}^{\ast }(o_h).$

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
${\delta }_{41}^{*}$	0.9769	1.0000	0.9586	0.6993	0.6815	0.6206
${\delta }_{42}^{*}$	0.9776	1.0000	0.9497	0.6998	0.6819	0.6211
${\delta }_{43}^{*}$	0.9776	1.0000	0.9497	0.6998	0.6819	0.6211
${\delta }_{45}^{*}$	0.9816	1.0000	0.9586	0.6993	0.7318	0.6206

Source: Ours.

Table 11. The modified weights ${\delta }_{5wh}^{\ast }(o_h).$

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
${\delta }_{51}^{*}$	0.9769	1.0000	0.9586	0.7474	0.6815	0.6206
${\delta }_{52}^{*}$	0.9776	1.0000	0.9497	0.7479	0.6819	0.6211
${\delta }_{53}^{*}$	0.9776	1.0000	0.9497	0.7479	0.6819	0.6211
${\delta }_{54}^{*}$	0.9776	1.0000	0.9497	0.7479	0.6819	0.6785

Source: Ours.

Table 12. Distance between each of the two alternatives.

	$F_1$	$F_2$	$F_3$	$F_4$	$F_5$	$F_6$
$d_h(J_1,J_2)$	0.1479	0.3793	0.3939	0.0220	0.1283	0.0874
$d_h(J_1,J_3)$	0.0463	0.3403	0.2891	0.0436	0.0592	0.1313
$d_h(J_1,J_4)$	0.0347	0.0695	0.1008	0.0537	0.0656	0.2381
$d_h(J_1,J_5)$	0.0856	0.0573	0.0637	0.1772	0.1194	0.1991
$d_h(J_2,J_3)$	0.1016	0.0390	0.1048	0.0285	0.0691	0.0440
$d_h(J_2,J_4)$	0.1689	0.3098	0.2931	0.0687	0.1939	0.1508
$d_h(J_2,J_5)$	0.2335	0.3220	0.3302	0.1621	0.2478	0.1118
$d_h(J_3,J_4)$	0.0673	0.2707	0.1883	0.0973	0.1248	0.1068
$d_h(J_3,J_5)$	0.1319	0.2829	0.2254	0.1336	0.1787	0.0678
$d_h(J_4,J_5)$	0.0659	0.0149	0.0371	0.2309	0.0539	0.0390

Source: Ours.

Table 13. The sequence from different methods.

Method	The sequence	The best alternative
SVNWA (Zhang et al., 2014)	$J_2>J_3>J_1>J_5>J_4$	$J_2$
SVNWG (Zhang et al., 2014)	$J_2>J_3>J_4>J_5>J_1$	$J_2$
Xu et al. (2017)	$J_2>J_3>J_1>J_5>J_4$	$J_2$
Nancy and Garg (2019)	$J_2>J_3>J_1>J_5>J_4$	$J_2$
Selvachandran et al. (2018)	$J_2>J_3>J_1>J_4>J_5$	$J_2$
Ye (2014)	$J_2>J_3>J_1>J_5>J_4$	$J_2$
Peng and Dai (2018)	$J_2>J_3>J_1>J_5>J_4$	$J_2$
CPT-SVN-TODIM	$J_2>J_3>J_1>J_5>J_4$	$J_2$

Source: Ours.

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