Table 2.

Comparison based on Eq. (8).

(a) The minimum value and JND threshold for each attribute
Ordered attributes m	Option A	Option B	Option C	$\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	${\beta }_m^{\mathit{JND}}$	${\beta }_m^{\mathit{JND}}\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$
Travel time (very important)	11.5 min	10 min	9 min	9 min	20%	1.8 min
Waiting time (important)	5 min	10 min	9 min	5 min	20%	1.0 min
Fare (least important)	$ 5	$ 4	$ 5	$ 4	10%	$ 0.4

(b) Compare A and B*
Ordered attributes m	Option A	Option B	$v_{l^{\prime },m}^{\mathit{od}}-\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Compare with${\beta }_m^{\mathit{JND}}\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Noticeable difference
Travel time (very important)	11.5 min	10 min	A: (11.5–9) = 2.5 min B: (10–9) =1.0 min	A: 2.5 >1.8 min B: 1.0 < 1.8 min	A: Yes B: No
Waiting time (important)	5 min	10 min	A: (5–5) = 0 min B: (10–5) = 5 min	A: 0 < 1.0 min B: 5 >1.0 min	A: No B: Yes
Fare (least important)	$ 5	$ 4	A: (5–4) = $ 1 B: (4–4) =$ 0	A: $1 > $ 0.4 B: $ 0 < $ 0.4	A: Yes B: No

(c) Compare B and C**
Ordered attributes m	Option B	Option C	$v_{l^{\prime },m}^{\mathit{od}}-\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Compare with${\beta }_m^{\mathit{JND}}\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Noticeable difference
Travel time (very important)	10 min	9 min	B: (10–9) = 1.0 min C: (9–9) = 0 min	B: 1.0 < 1.8 min C: 0 < 1.8 min	B: No C: No
Waiting time (important)	10 min	9 min	B: (10–5) = 5 min C: (9–5) = 4 min	B: 5 > 1.0 min C: 4 >1.0 min	B: Yes C: Yes
Fare (least important)	$ 4	$ 5	B: (4–4) = $ 0 C: (5–4) =$ 1	B: $1 > $ 0.4 C: $ 0 < $ 0.4	B: Yes C: No

(d) Compare A and C***
Ordered attributes m	Option A	Option C	$v_{l^{\prime },m}^{\mathit{od}}-\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Compare with${\beta }_m^{\mathit{JND}}\underset{\overline{l}\in L^{\mathit{od}}}{min}\left\{v_{\overline{l},m}^{\mathit{od}}\right\}$	Noticeable difference
Travel time (very important)	11.5 min	9 min	A: (11.5–9) = 2.5 min C: (9–9) = 0 min	A: 2.5 >1.8 min C: 0 < 1.8 min	A: Yes C: No
Waiting time (important)	5 min	9 min	A: (5–5) = 0 min C: (9–5) = 4 min	A: 0 < 1.0 min C: 4 >1.0 min	A: No C: Yes
Fare (least important)	$ 5	$ 5	A: (5–4) = $ 1 C: (5–4) =$ 1	A: $1 > $ 0.4 C: $ 0 < $ 0.4	A: Yes C: No

^*It is concluded from the table that $B\underset{\_}{\succ }A$ because of noticed difference between travel times (and the least is noticed for B).

^**It is concluded from the table that $C\underset{\_}{\succ }B$ because of noticed difference between waiting times (and the least is noted for C).

^***It is concluded from the table that $C\underset{\_}{\succ }A$ because of noticed differences between travel times (and the least is noted for C).