Table 2. (a) P matrix, (b) Z matrix and...

Table 2.

(a) P matrix, (b) Z matrix and (c) scaling resulting from the application of the proposed procedure to the case study

	S₁	S₂	S₃	S₄	S₅	S₆	S₇	S₈	S_∅	S_△	S_○	S_●
(a) P matrix
S₁	0.500	0.195	0.250	0.535	0.140	0.305	0.125	0.415	0.570	0.140	0.140	0.070
S₂	0.805	0.500	0.490	0.805	0.475	0.375	0.220	0.620	0.675	0.555	0.275	0.050
S₃	0.750	0.490	0.500	0.250	0.514	0.615	0.360	0.290	0.180	0.760	0.810	0.070
S₄	0.430	0.195	0.250	0.500	0.070	0.235	0.055	0.250	0.570	0.140	0.070	0.000
S₅	0.860	0.525	0.514	0.930	0.500	0.400	0.475	0.890	1.000	0.945	0.445	0.000
S₆	0.695	0.625	0.615	0.765	0.600	0.500	0.585	0.780	0.945	0.670	0.600	0.265
S₇	0.875	0.780	0.360	0.945	0.525	0.415	0.500	0.790	0.945	0.790	0.525	0.180
S₈	0.585	0.380	0.290	0.750	0.110	0.220	0.210	0.500	0.655	0.210	0.110	0.055
S_∅	0.430	0.325	0.180	0.543	0.000	0.055	0.055	0.345	0.500	0.000	0.000	0.000
S_△	0.860	0.455	0.765	0.860	0.055	0.330	0.210	0.790	1.000	0.500	0.000	0.000
S_○	0.860	0.695	0.810	0.930	0.555	0.400	0.475	0.890	1.000	1.000	0.500	0.000
S_●	0.930	0.950	0.930	1.000	1.000	0.735	0.820	0.945	1.000	1.000	1.000	0.500
(b) Z matrix
S₁	0.000	0.859	0.674	−0.176	1.080	0.510	1.150	0.125	−0.176	1.080	1.080	1.476
S₂	−0.859	0.000	0.025	−0.859	0.062	−0.318	0.772	−0.305	−0.455	−0.125	0.597	1.281
S₃	−0.675	−0.025	0.000	−0.674	0.035	0.292	−0.358	−0.553	−0.915	−0.214	−0.075	−0.974
S₄	0.176	0.859	0.674	0.000	1.475	0.722	1.598	0.675	−0.176	1.080	1.476	3.000
S₅	−1.080	−0.062	−0.035	−1.475	0.000	0.253	0.063	−1.227	−3.000	−1.598	0.138	3.000
S₆	−0.510	−0.318	−0.292	−0.722	−0.253	0.000	−0.215	−0.772	−1.598	−0.439	−0.253	0.628
S₇	−1.150	−0.772	−0.358	−1.598	−0.063	0.215	0.000	−0.806	−1.598	−0.806	−0.063	0.915
S₈	−0.214	0.305	0.553	−0.674	1.227	0.772	0.806	0.000	−0.399	0.806	1.227	1.598
S_∅	0.176	0.453	0.915	0.176	−3.000	1.598	1.598	0.399	0.000	3.000	3.000	3.000
S_△	−1.080	0.125	0.214	−1.080	1.598	0.439	0.806	−0.806	−3.000	0.000	3.000	3.000
S_○	−1.080	−0.597	0.074	−1.476	−0.138	0.253	−0.063	−1.226	−3.000	−3.000	0.000	3.000
S_●	−1.476	−1.281	−0.874	−3.000	−3.000	−0.628	−0.915	−1.599	−3.000	−3.000	−3.000	0.000
(c) Scaling
Σ_k	−7.773	−0.453	2.23	−11.56	−0.977	4.108	5.242	−6.095	−17.317	−3.216	7.127	19.924
x_k	−0.647	−0.037	0.185	−0.963	−0.081	0.342	0.437	−0.508	−1.443	−0.268	0.594	1.667
y_k	2.56	4.53	5.25	1.55	4.39	5.75	6.06	3.01	0	3.78	6.56	10

	S₁	S₂	S₃	S₄	S₅	S₆	S₇	S₈	S_∅	S_△	S_○	S_●
(a) P matrix
S₁	0.500	0.195	0.250	0.535	0.140	0.305	0.125	0.415	0.570	0.140	0.140	0.070
S₂	0.805	0.500	0.490	0.805	0.475	0.375	0.220	0.620	0.675	0.555	0.275	0.050
S₃	0.750	0.490	0.500	0.250	0.514	0.615	0.360	0.290	0.180	0.760	0.810	0.070
S₄	0.430	0.195	0.250	0.500	0.070	0.235	0.055	0.250	0.570	0.140	0.070	0.000
S₅	0.860	0.525	0.514	0.930	0.500	0.400	0.475	0.890	1.000	0.945	0.445	0.000
S₆	0.695	0.625	0.615	0.765	0.600	0.500	0.585	0.780	0.945	0.670	0.600	0.265
S₇	0.875	0.780	0.360	0.945	0.525	0.415	0.500	0.790	0.945	0.790	0.525	0.180
S₈	0.585	0.380	0.290	0.750	0.110	0.220	0.210	0.500	0.655	0.210	0.110	0.055
S_∅	0.430	0.325	0.180	0.543	0.000	0.055	0.055	0.345	0.500	0.000	0.000	0.000
S_△	0.860	0.455	0.765	0.860	0.055	0.330	0.210	0.790	1.000	0.500	0.000	0.000
S_○	0.860	0.695	0.810	0.930	0.555	0.400	0.475	0.890	1.000	1.000	0.500	0.000
S_●	0.930	0.950	0.930	1.000	1.000	0.735	0.820	0.945	1.000	1.000	1.000	0.500
(b) Z matrix
S₁	0.000	0.859	0.674	−0.176	1.080	0.510	1.150	0.125	−0.176	1.080	1.080	1.476
S₂	−0.859	0.000	0.025	−0.859	0.062	−0.318	0.772	−0.305	−0.455	−0.125	0.597	1.281
S₃	−0.675	−0.025	0.000	−0.674	0.035	0.292	−0.358	−0.553	−0.915	−0.214	−0.075	−0.974
S₄	0.176	0.859	0.674	0.000	1.475	0.722	1.598	0.675	−0.176	1.080	1.476	3.000
S₅	−1.080	−0.062	−0.035	−1.475	0.000	0.253	0.063	−1.227	−3.000	−1.598	0.138	3.000
S₆	−0.510	−0.318	−0.292	−0.722	−0.253	0.000	−0.215	−0.772	−1.598	−0.439	−0.253	0.628
S₇	−1.150	−0.772	−0.358	−1.598	−0.063	0.215	0.000	−0.806	−1.598	−0.806	−0.063	0.915
S₈	−0.214	0.305	0.553	−0.674	1.227	0.772	0.806	0.000	−0.399	0.806	1.227	1.598
S_∅	0.176	0.453	0.915	0.176	−3.000	1.598	1.598	0.399	0.000	3.000	3.000	3.000
S_△	−1.080	0.125	0.214	−1.080	1.598	0.439	0.806	−0.806	−3.000	0.000	3.000	3.000
S_○	−1.080	−0.597	0.074	−1.476	−0.138	0.253	−0.063	−1.226	−3.000	−3.000	0.000	3.000
S_●	−1.476	−1.281	−0.874	−3.000	−3.000	−0.628	−0.915	−1.599	−3.000	−3.000	−3.000	0.000
(c) Scaling
Σ_k	−7.773	−0.453	2.23	−11.56	−0.977	4.108	5.242	−6.095	−17.317	−3.216	7.127	19.924
x_k	−0.647	−0.037	0.185	−0.963	−0.081	0.342	0.437	−0.508	−1.443	−0.268	0.594	1.667
y_k	2.56	4.53	5.25	1.55	4.39	5.75	6.06	3.01	0	3.78	6.56	10

Note(s):

Σ_k is the summation of the values reported in the kth column of the Z matrix; the x_k values concern the interval scaling resulting from the Thurstone’s LCJ; the y_k values concern the ratio scaling downstream of the anchoring in equation (4)

Source(s): Table created by authors

[ViewLarge]

Sharing Unavailable