Table 4 AHP-BWM simulation results on...

Table 4

AHP-BWM simulation results on minimum violation (⁠ $M V$ ⁠) (as % of number of simulations)

	Observations
	5	10	15	20	25	30	35	40	45	50	60	70	80	90	100
4A. Equal performance (⁠ ${M V}_{A H P ‐ B W M} = {M V}_{A H P}$ ⁠)
$K = 100$	81.5	72.0	61.0	53.0	44.0	38.5	34.0	31.5	27.5	25.8	19.8	18.0	15.0	11.8	8.75
$K = 300$	81.8	69.7	60.2	53.1	46.0	41.2	35.4	28.1	24.8	23.2	19.9	17.3	14.1	12.2	10.1
$K = 500$	82.6	71.7	59.1	49.0	45.0	40.0	35.2	30.9	26.2	24.7	21.6	15.4	13.7	11.5	9.9
$K = 1000$	82.1	69.7	60.2	50.9	45.4	40.8	34.5	29.9	26.4	24.3	20.5	17.5	13.7	10.8	9.75
4B. AHP-BWM outperforms AHP (⁠ ${M V}_{A H P ‐ B W M} < {M V}_{A H P}$ ⁠)
$K = 100$	16.0	26.5	38.8	46.8	55.8	61.5	66.0	68.0	72.3	74.3	80.3	81.3	85.0	88.0	91.0
$K = 300$	14.9	29.5	39.2	46.4	53.7	58.7	64.4	71.9	74.6	76.8	79.8	82.3	85.8	87.8	89.7
$K = 500$	15.1	27.7	40.5	50.6	54.6	59.9	64.7	68.9	73.8	75.1	78.3	84.4	86.3	88.3	89.8
$K = 1000$	15.3	29.3	39.4	48.5	54.4	59.1	65.3	70.0	73.4	75.6	79.4	82.4	86.2	89.0	89.9
4C. AHP outperforms AHP-BWM (⁠ ${M V}_{A H P} < {M V}_{A H P ‐ B W M}$ ⁠)
$K = 100$	2.5	1.5	0.2	0.2	0.2	0	0	0.5	0.2	0	0	0.7	0	0.2	0.2
$K = 300$	3.3	0.8	0.7	0.5	0.3	0.2	0.2	0	0.6	0	0.3	0.4	0.2	0.1	0.2
$K = 500$	2.4	0.7	0.4	0.4	0.4	0.2	0.15	0.2	0.1	0.2	0.2	0.2	0.1	0.3	0.3
$K = 1000$	2.7	1.0	0.5	0.6	0.2	0.2	0.23	0.2	0.2	0.2	0.2	0.2	0.1	0.2	0.3

	Observations
	5	10	15	20	25	30	35	40	45	50	60	70	80	90	100
4A. Equal performance ( ${M V}_{A H P ‐ B W M} = {M V}_{A H P}$ )
$K = 100$	81.5	72.0	61.0	53.0	44.0	38.5	34.0	31.5	27.5	25.8	19.8	18.0	15.0	11.8	8.75
$K = 300$	81.8	69.7	60.2	53.1	46.0	41.2	35.4	28.1	24.8	23.2	19.9	17.3	14.1	12.2	10.1
$K = 500$	82.6	71.7	59.1	49.0	45.0	40.0	35.2	30.9	26.2	24.7	21.6	15.4	13.7	11.5	9.9
$K = 1000$	82.1	69.7	60.2	50.9	45.4	40.8	34.5	29.9	26.4	24.3	20.5	17.5	13.7	10.8	9.75
4B. AHP-BWM outperforms AHP ( ${M V}_{A H P ‐ B W M} < {M V}_{A H P}$ )
$K = 100$	16.0	26.5	38.8	46.8	55.8	61.5	66.0	68.0	72.3	74.3	80.3	81.3	85.0	88.0	91.0
$K = 300$	14.9	29.5	39.2	46.4	53.7	58.7	64.4	71.9	74.6	76.8	79.8	82.3	85.8	87.8	89.7
$K = 500$	15.1	27.7	40.5	50.6	54.6	59.9	64.7	68.9	73.8	75.1	78.3	84.4	86.3	88.3	89.8
$K = 1000$	15.3	29.3	39.4	48.5	54.4	59.1	65.3	70.0	73.4	75.6	79.4	82.4	86.2	89.0	89.9
4C. AHP outperforms AHP-BWM ( ${M V}_{A H P} < {M V}_{A H P ‐ B W M}$ )
$K = 100$	2.5	1.5	0.2	0.2	0.2	0	0	0.5	0.2	0	0	0.7	0	0.2	0.2
$K = 300$	3.3	0.8	0.7	0.5	0.3	0.2	0.2	0	0.6	0	0.3	0.4	0.2	0.1	0.2
$K = 500$	2.4	0.7	0.4	0.4	0.4	0.2	0.15	0.2	0.1	0.2	0.2	0.2	0.1	0.3	0.3
$K = 1000$	2.7	1.0	0.5	0.6	0.2	0.2	0.23	0.2	0.2	0.2	0.2	0.2	0.1	0.2	0.3

Note(s): This table presents the minimum violation (⁠ $M V$ ⁠) comparison between AHP and AHP-BWM using the full simulation of 5,130,000 comparison matrices. $O b s e r v a t i o n s$ represents the group size of the number of alternatives, and $K$ denotes the number of simulations

The sums of some indicators in this table may not equal 100% due to the number's rounding issue

Source(s): Author’s own work

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