Dynamic reference point method with probabilistic linguistic information based on the regret theory for public health emergency decision-making

Figures & data

Figure 1. The modified value function $\overline{v}(r^{(l)})$ when $\tau =3.$

Source: Authors' calculation.

Figure 2. The modified regret-rejoice function $R(\Delta H)$ when $\tau =3.$

Source: Authors' calculation.

Figure 3. A framework of the PLDPR method.

Source: Authors' calculation.

Table 1. Evaluation information of $H_{t_1}.$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	$\left\{s_1(0.2),s_2(0.8)\right\}$	$\left\{s_{-1}(0.3),s_0(0.7)\right\}$	$\left\{s_0(0.5),s_1(0.5)\right\}$	$\left\{s_0(0.6),s_1(0.4)\right\}$
$d_2$	$\left\{s_0(0.3),s_1(0.6)\right\}$	$\left\{s_1(0.5),s_2(0.4)\right\}$	$\left\{s_0(0.6),s_1(0.3)\right\}$	$\left\{s_{-1}(0.3),s_0(0.4),s_1(0.3)\right\}$
$d_3$	$\left\{s_1(0.8),s_2(0.2)\right\}$	$\left\{s_0(0.9)\right\}$	$\left\{s_1(0.4),s_2(0.6)\right\}$	$\left\{s_2(0.5),s_3(0.5)\right\}$
$d_4$	$\left\{s_0(0.7),s_1(0.3)\right\}$	$\left\{s_{-1}(0.6),s_0(0.3)\right\}$	$\left\{s_1(0.2),s_2(0.5),s_3(0.3)\right\}$	$\left\{s_1(0.9),s_2(0.1)\right\}$
$d_5$	$\left\{s_1(0.5),s_2(0.5)\right\}$	$\left\{s_1(0.7),s_2(0.2)\right\}$	$\left\{s_2(0.6),s_3(0.4)\right\}$	$\left\{s_{-1}(0.5),s_0(0.4)\right\}$

Source: Authors' calculation.

Table 2. Evaluation information of $H_{t_2}.$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	$\left\{s_2(0.3),s_3(0.7)\right\}$	$\left\{s_{-2}(0.4),s_{-1}(0.6)\right\}$	$\left\{s_0(0.5),s_1(0.5)\right\}$	$\left\{s_{-1}(0.5),s_0(0.4)\right\}$
$d_2$	$\left\{s_0(0.6),s_1(0.4)\right\}$	$\left\{s_1(0.3),s_2(0.7)\right\}$	$\left\{s_1(0.4),s_2(0.6)\right\}$	$\left\{s_0(0.4),s_1(0.5)\right\}$
$d_3$	$\left\{s_1(0.6),s_2(0.4)\right\}$	$\left\{s_3(0.9)\right\}$	$\left\{s_1(0.3),s_2(0.7)\right\}$	$\left\{s_2(0.2),s_3(0.8)\right\}$
$d_4$	$\left\{s_{-1}(0.5),s_0(0.5)\right\}$	$\left\{s_{-1}(0.7),s_0(0.2)\right\}$	$\left\{s_1(0.5),s_2(0.5)\right\}$	$\left\{s_1(0.5),s_2(0.4)\right\}$
$d_5$	$\left\{s_1(0.4),s_2(0.5)\right\}$	$\left\{s_2(0.4),s_3(0.5)\right\}$	$\left\{s_1(0.5),s_2(0.4)\right\}$	$\left\{s_0(0.4),s_1(0.6)\right\}$

Source: Authors' calculation.

Table 3. Evaluation information of $H_{t_3}.$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	$\left\{s_2(0.6),s_3(0.4)\right\}$	$\left\{s_0(0.6),s_1(0.4)\right\}$	$\left\{s_0(0.5),s_1(0.5)\right\}$	$\left\{s_1(0.5),s_2(0.4)\right\}$
$d_2$	$\left\{s_0(0.6),s_1(0.4)\right\}$	$\left\{s_1(0.3),s_2(0.7)\right\}$	$\left\{s_{-1}(0.6),s_0(0.4)\right\}$	$\left\{s_1(0.4),s_2(0.5)\right\}$
$d_3$	$\left\{s_1(0.6),s_2(0.4)\right\}$	$\left\{s_1(0.2),s_2(0.8)\right\}$	$\left\{s_0(0.3),s_1(0.7)\right\}$	$\left\{s_0(0.2),s_1(0.8)\right\}$
$d_4$	$\left\{s_0(0.7),s_1(0.2)\right\}$	$\left\{s_1(0.7),s_2(0.2)\right\}$	$\left\{s_0(0.5),s_1(0.5)\right\}$	$\left\{s_1(0.5),s_2(0.4)\right\}$
$d_5$	$\left\{s_1(0.4),s_2(0.5)\right\}$	$\left\{s_1(0.4),s_2(0.5)\right\}$	$\left\{s_0(0.5),s_1(0.4)\right\}$	$\left\{s_2(0.2),s_3(0.8)\right\}$

Source: Authors' calculation.

Table 4. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_1,{\overline{h}}_S^{ij}{(p)}^{+}|t_1).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	0.7975	1.0600	0.9358	0.9493
$d_2$	0.9167	0.8007	0.9564	1.0296
$d_3$	0.8410	1.0188	0.7996	0.6912
$d_4$	0.9648	1.1286	0.4655	0.8545
$d_5$	0.8025	0.8308	0.6938	1.1160

Source: Authors' calculation.

Table 5. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_1,{\overline{h}}_S^{ij}{(p)}^{-}|t_1).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	0.6828	0.2844	0.4181	0.3979
$d_2$	0.4492	0.5747	0.3879	0.4137
$d_3$	0.5219	0.3160	0.6054	0.7502
$d_4$	0.3770	0.2681	1.0929	0.5246
$d_5$	0.5799	0.5305	0.7297	0.2642

Source: Authors' calculation.

Table 6. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_2,{\overline{h}}_S^{ij}{(p)}^{+}|t_2).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	0.7649	2.2023	1.2748	1.7962
$d_2$	1.3153	0.8515	0.8062	1.2555
$d_3$	0.8062	1.0713	0.8515	1.0050
$d_4$	1.7678	1.9121	0.7906	0.7945
$d_5$	0.7945	0.4373	0.7945	1.2369

Source: Authors' calculation.

Table 7. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_2,{\overline{h}}_S^{ij}{(p)}^{-}|t_2).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	2.4668	0.3162	1.2748	0.7754
$d_2$	1.2166	1.9300	1.8439	1.3043
$d_3$	1.7029	1.7653	1.9300	2.6000
$d_4$	0.7906	0.7289	1.7678	1.7339
$d_5$	1.8045	2.3057	1.7339	1.3342

Source: Authors' calculation.

Table 8. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_3,{\overline{h}}_S^{ij}{(p)}^{+}|t_3).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	0.3000	1.3153	1.2748	0.7945
$d_2$	1.3153	0.8515	1.8248	0.7945
$d_3$	0.8062	0.9220	1.2021	1.1705
$d_4$	1.3807	0.8839	1.2748	0.7945
$d_5$	0.7945	0.7945	1.2947	1.0050

Source: Authors' calculation.

Table 9. The deviation degrees $d({\overline{h}}_S^{ij}(p)|t_3,{\overline{h}}_S^{ij}{(p)}^{-}|t_3).$

	$A_1$	$A_2$	$A_3$	$A_4$
$d_1$	1.7000	0.7280	0.7906	1.2374
$d_2$	0.7280	1.4577	0.3606	1.3158
$d_3$	1.2042	1.5652	0.9192	0.9849
$d_4$	0.6374	1.1319	0.7906	1.2374
$d_5$	1.3158	1.3158	0.7591	2.1471

Source: Authors' calculation.

Table 10. The results of comparison.

	$t_1$	$t_2$	$t_3$
The PLDRP method	$A_3\succ A_1\succ A_4\succ A_2$	$A_3\succ A_4\succ A_1\succ A_2$	$A_4\succ A_1\succ A_2\succ A_3$
The PLDRP method without regret theory	$A_3\succ A_4\succ A_1\succ A_2$	$A_3\succ A_4\succ A_2\succ A_1$	$A_4\succ A_2\succ A_1\succ A_3$
The PLWA operator	$A_3\succ A_1\succ A_4\succ A_2$	$A_3\succ A_1\succ A_2\succ A_4$	$A_4\succ A_2\succ A_1\succ A_3$

Source: Authors' calculation.