A methodology for weighting indicators of value assessment of historic building using AHP with experts’ priorities

Figures & data

Table 1. The numerical values and the corresponding dominant intensities in pairwise comparison judgments.

Values of a^eij	Corresponding intensities of the dominant
1	Indicator i and indicator j are of equal importance.
3	Indicator i moderately dominant indicator j.
5	Indicator i strongly dominant indicator j.
7	Indicator i very strongly dominant indicator j.
9	Indicator i extremely dominant indicator j.
2,4,6,8	Intermediate values between the above pairs of adjacent judgments.

Table 2. Random Index (R.I.) of consistency estimation according to matrix size covering this study.

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
R.I.	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.48	1.56	1.57	1.59

Table 3. Frame of indicators for value assessment of historic building in Hangzhou city China.

Category	Indicator	Explanation of indicator
A. Historic value	A1. The age	A1.The period of time from its construction to assessing date.
	A2. Relevance to historic personage or event	A2. The building is relevant to a historic personage or a historic event, for example, the personage was born in this building, or the historic event happened in this building.
	A3. Record of history of the city	A3.The building witnesses the local history of townscape, or handicraft, or industry, or life style.
	A4. Authenticity	A4.The quality of convincing evidences of historic information of the building.
B. Cultural &Artistic value	B1. Representative of an architectural style	B1.The building is a typical case of an architectural style, recognized in such as the façade, colour, or shape.
	B2. Architectural decoration	B2.The amounts and the exquisite intensities of architectural decorations of the building.
	B3. Emotional issue	B3.The building plays a role in the psychological identity or the collective memory of the residents in this city.
	B4. Relevance to local culture or custom	B4.The building is relevant to the local cultural characteristics, the local ideology, or the local traditional custom, typically, the building was constructed for a ceremony of the local custom.
C. Scientific value	C1. Architectural design	C1.The optimization of the site selection, the layout, the spatial design, or the facilities installed.
	C2. Architectural structure	C2.The originality of structure (based on the construction time), or representative of a local traditional structure, or the rarity of structure in current buildings.
	C3. Construction technique	C3.The advancement of construction techniques used in the building (based on the construction time).
	C4. Material	C4.The quality and the rarity of materials used in the building.
D. Environmental Value	D1. Relevance to the local environment	D1.The building relates to the local environment including the West Lake landscape and the Beijing-Hangzhou Grand Canal.
	D2. Relevance to a preserved area	D2. The building relates to an officially listed preserved area.
	D3. Relevance to the current local townscape	D3.The building plays a unique role in the current townscape of this city.
E. Practical value	E1. Current integrity	E1.The consistent scale of construction between the current building and the initial building .
	E2. Practical utilization	E2.The potential practical utilization of the building in the future.
	E3. Current quality	E3.The current quality of the building includes the solidness of structure, the performance of envelopes, and the facilities.

Figure 1. An example part of questionnaire.

Figure 2. Comparison matrices of individual expert P_1.

Figure 3. Consistent estimation of the comparison matrices of individual expert P_1.

Figure 4. The comparison matrices of group decision by assigning experts’ priorities averagely.

Figure 5. Consistent estimation of comparison matrices of group decision by assigning experts’ priorities averagely.

Table 4. Normalization weights of indicators by method 1 (U_a).

Indicator	A1	A2	A3	A4	B1	B2	B3	B4	C1	C2	C3	C4	D1	D2	D3	E1	E2	E3	sum
Weights	0.093	0.109	0.080	0.131	0.097	0.050	0.044	0.072	0.074	0.046	0.033	0.023	0.035	0.028	0.025	0.035	0.010	0.015	1.000

Table 5. The d_xy according to the iterative clustering steps.

Step1	Step2	Step3	Step4	Step5	Step6	Step7	Step8	Step9	Step10	Step11	Step12
0.9674	0.9655	0.9630	0.9621	0.9563	0.9545	0.9529	0.9506	0.9504	0.9484	0.9463	0.9462
Step13	Step14	Step15	Step16	Step17	Step18	Step19	Step20	Step21	Step22	Step23	Step24
0.9443	0.9437	0.9377	0.9354	0.9346	0.9271	0.9220	0.9219	0.9191	0.9181	0.9167	0.9111

Table 6. Normalization priorities of experts by iterative clustering analysis.

w1	w2	w3	w4	w5	w6	w7	w8	w9	w10	w11	w12	w13	w14	w15
0.0039	0.0232	0.0039	0.0039	0.0039	0.0039	0.0232	0.0039	0.0039	0.0425	0.0039	0.0347	0.0039	0.0039	0.0232
w16	w17	w18	w19	w20	w21	w22	w23	w24	w25	w26	w27	w28	w29	w30
0.0039	0.0347	0.0039	0.0425	0.0232	0.0077	0.0425	0.0347	0.0425	0.0039	0.0425	0.0347	0.0232	0.0347	0.0347
w31	w32	w33	w34	w35	w36	w37	w38	w39	w40	w41	w42	w43	w44	w45
0.0347	0.0425	0.0425	0.0039	0.0425	0.0425	0.0347	0.0039	0.0347	0.0425	0.0039	0.0039	0.0232	0.0425	0.0077

Figure 6. The iterative clustering process.

Figure 7. The group comparison matrices by assigning experts’ priorities based on iterative clustering analysis.

Figure 8. Consistent estimation of comparison matrices of group decision by assigning experts’ priorities based on iterative clustering analysis.

Table 7. Normalization weights of indicators by method 2 (U_b).

Indicator	A1	A2	A3	A4	B1	B2	B3	B4	C1	C2	C3	C4	D1	D2	D3	E1	E2	E3	sum
Weights	0.132	0.119	0.075	0.140	0.091	0.043	0.040	0.057	0.072	0.045	0.028	0.019	0.032	0.026	0.022	0.034	0.011	0.015	1.000

Table 8. Sequential number of experts (y_e).

y1	y2	y3	y4	y5	y6	y7	y8	y9	y10	y11	y12	y13	y14	y15
1	14	41	4	7	35	31	3	2	13	9	38	32	12	21
y16	y17	y18	y19	y20	y21	y22	y23	y24	y25	y26	y27	y28	y29	y30
25	29	16	28	19	8	43	45	22	34	30	10	33	15	18
y31	y32	y33	y34	y35	y36	y37	y38	y39	y40	y41	y42	y43	y44	y45
39	6	42	26	23	17	37	24	44	5	27	11	40	36	20

Figure 9. The group comparison matrices by assigning experts’ priorities based on sequential analysis.

Figure 10. Consistent estimation of comparison matrices of group decision by assigning experts’ priorities based on sequential analysis.

Table 9. Normalization priorities of experts by sequential analysis (β_e).

β1	β2	β3	β4	β5	β6	β7	β8	β9	β10	β11	β12	β13	β14	β15
0.0000	0.0062	0.0535	0.0005	0.0016	0.0390	0.0306	0.0003	0.0001	0.0054	0.0026	0.0460	0.0326	0.0046	0.0140
β16	β17	β18	β19	β20	β21	β22	β23	β24	β25	β26	β27	β28	β29	β30
0.0199	0.0268	0.0082	0.0250	0.0115	0.0021	0.0589	0.0645	0.0154	0.0368	0.0287	0.0032	0.0347	0.0072	0.0103
β31	β32	β33	β34	β35	β36	β37	β38	β39	β40	β41	β42	β43	β44	β45
0.0484	0.001	0.0562	0.0215	0.0168	0.0092	0.0436	0.0183	0.0617	0.0008	0.0232	0.0039	0.0510	0.0413	0.0127

Table 10. Normalization weights of indicators by method 3 (U_c).

Indicator	A1	A2	A3	A4	B1	B2	B3	B4	C1	C2	C3	C4	D1	D2	D3	E1	E2	E3	sum
Weights	0.090	0.126	0.071	0.133	0.098	0.048	0.040	0.061	0.077	0.050	0.036	0.024	0.036	0.027	0.025	0.033	0.012	0.014	1.000

Figure 11. Normalization weights of indicators by expert P_1.

Figure 12. Normalization weights of indicators by expert P_22.

Figure 13. Normalization weights of indicators by method 1.

Figure 14. Normalization weights of indicators by method 2.

Figure 15. Normalization weights of indicators by method 3.

Figure 16. The identification of experts with extremal preference by method 2 and method 3.

Figure 17. The priorities of 9 experts with extremal preference identified by method 2 and method 3.