Table 3 AHP-BWM simulation results on...

Table 3

AHP-BWM simulation results on consistency ratio (⁠ $C R$ ⁠) (as % of number of simulations)

${C R}_{A H P ‐ B W M} < {C R}_{A H P}$	Observations
${C R}_{A H P ‐ B W M} < {C R}_{A H P}$	5	10	15	20	25	30	35	40	45	50	60	70	80	90	100
$C r i t e r i a = 3$
$K = 100$	4.0	8.0	14.0	18.0	28.0	22.0	36.0	41.0	44.0	51.0	70	70	81.0	83.0	85.0
$K = 300$	4.0	7.0	11.7	17.0	24.0	29.7	35.0	45.0	48.7	53.3	58.3	67.7	81.0	83.7	89.3
$K = 500$	4.2	8.8	12.4	18.8	24.0	31.4	35.8	41.4	44.6	51.4	60.4	71.8	82.6	84.0	87.8
$K = 1000$	3.7	9.7	12.6	17.6	25.4	31.6	40.2	40.7	47.9	53.1	62.6	69.7	81.4	86.1	87.3
$C r i t e r i a = 4$
$K = 100$	63.0	91.0	98.0	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	61.3	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	52.2	96.8	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	59.4	96.0	99.6	100	100	100	100	100	100	100	100	100	100	100	100
$C r i t e r i a = 5$
$K = 100$	99.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	96.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$C r i t e r i a = 6$
$K = 100$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100

${C R}_{A H P ‐ B W M} < {C R}_{A H P}$	Observations
$C r i t e r i a = 3$
$K = 100$	4.0	8.0	14.0	18.0	28.0	22.0	36.0	41.0	44.0	51.0	70	70	81.0	83.0	85.0
$K = 300$	4.0	7.0	11.7	17.0	24.0	29.7	35.0	45.0	48.7	53.3	58.3	67.7	81.0	83.7	89.3
$K = 500$	4.2	8.8	12.4	18.8	24.0	31.4	35.8	41.4	44.6	51.4	60.4	71.8	82.6	84.0	87.8
$K = 1000$	3.7	9.7	12.6	17.6	25.4	31.6	40.2	40.7	47.9	53.1	62.6	69.7	81.4	86.1	87.3
$C r i t e r i a = 4$
$K = 100$	63.0	91.0	98.0	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	61.3	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	52.2	96.8	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	59.4	96.0	99.6	100	100	100	100	100	100	100	100	100	100	100	100
$C r i t e r i a = 5$
$K = 100$	99.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	96.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	97.0	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$C r i t e r i a = 6$
$K = 100$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 300$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 500$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
$K = 1000$	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100

Note(s): This table presents the simulation results where the consistency ratio (⁠ $C R$ ⁠) derived by AHP-BWM is smaller than those derived by AHP, i.e. AHP-BWM produces more reliable results than AHP. $C r i t e r i a$ represents the dimension of the 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

Source(s): Author’s own work

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