Comparative Analysis of Multi-Criteria Methods for the Enhancement of Historical Buildings
Abstract
:1. Introduction
2. Aim of the Paper
3. MCDM Methods Comparative Analysis
- -
- Positive—that is, all the principal minors are positive, where by ‘principal minor’, we mean the determinant of the square sub-matrix formed by the first n rows and m columns (with 1 ≤ m ≤ n);
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- Reciprocal, being aij = 1/aji and therefore, the elements on the main diagonal are all unitary (aii = 1). This relationship of reciprocity arises from the need to guarantee the symmetry of judgments of importance;
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- Constituted by finite elements, since for each criterion, C, considered, we have aij ≠ ∞.
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- CR < 5% for n = 3;
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- CR < 9% for n = 4;
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- CR < 10% for n > 4.
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- Acceptable advantage, Q (A″) − Q (A′) ≥ DQ, with DQ = 1/(n − 1), where n is the number of alternatives;
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- Acceptable stability of the decision, that is, the alternative A′ must also be the best, or in the ranking must present the minimum value in terms of Si and/or Ri.
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- Alternatives A′ and A″, if only condition 2 is not satisfied;
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- Alternatives A′, A″, ..., AN, if only condition 1 is not met.
4. Selection of the Best Use of a Historic Building. Characterization of a Hierarchical Analysis Model
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- Community involvement (C1), intended as the average number of daily users. It is measured as the average daily number of people who attend the structure;
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- New workers (C2), measured as the number of new workers in the structure.
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- The cultural criterion includes the sub-criteria:
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- Cultural effects (C3), understood as the attraction of the structure with respect to cultural events;
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- Compatibility of the function with the historical-architectural characteristics of the property (C4). This criterion depends on the three sub-criteria:
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- Representativeness of the use function (C41), evaluated as the aptitude to express the cultural peculiarities of the reference territory, in respect of the material and spiritual reality of the architectural artefact;
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- Residential impact (C42), understood as the average number of daily users, in this case with a negative meaning, in the sense that higher this number is, the lower the score attributed to the alternative is. In fact, with the aim of protecting the cultural asset, it is advisable to prefer functional activities with a moderate residential impact, in order to avoid excessive loads on the structure that may require interventions of static adaptation such as to compromise the authenticity of the historical matter;
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- Respect of the criterion of minimum intervention (C43), that is, safeguarding the characteristics of the building. It is necessary to avoid intrusive interventions, such as new openings, tracks for installations, partitions, kitchens, and toilets, so as not to reduce the artistic-monumental quality of the property. This criterion represents one of the cardinal principles of architectural restoration and conservation of historic buildings. It is therefore a qualitative, rather than a quantitative criterion [49,50].
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- Return On Investment (C5). This is measured by ROI (Return On Investment), which expresses the rate of return on the total investments of a company for the assumed activity.
5. Case Study and Results
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- Bed & Breakfast (A1);
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- Multi-purpose rooms (A2) for holding conferences, seminars, thematic meetings, exhibitions and multimedia workshops;
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- Local cuisine restaurant (A3), which proposes traditional dishes, cooking workshops, as well as workshops for the valorization of the typical craftsmanship of the places, with an adjoining museum of rural civilization;
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- Public and private offices (A4).
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- Community involvement (C1). As there is no data on the average number of users, a filling index was envisaged as a rate of the maximum capacity of the structure;
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- New workers (C2). This data was obtained through surveys carried out in similar structures in the territory;
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- Cultural effects (C3). This is expressed as the ratio between the surface used for cultural activities (SC) and the total area of the building (ST);
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- Compatibility of the function with the historical-architectural characteristics of the property (C4). This criterion depends on the three sub-criteria:
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- Representativeness of the use function (C41), according to a judgment scale from 1–7;
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- Residential impact (C42), assessed as for criterion C1;
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- Respect of the criterion of minimum intervention (C43). The judgment was assigned by the decision-maker according to a qualitative scale from 1–7, depending on the level of protection that is guaranteed to the original structure;
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- Return On Investment, ROI (C5). For each of the four alternatives, the ROI value was derived from information on the profitability of the reference economic sector in the area of investigation.
6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
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n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
RCI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 |
Method | Number of Criteria | Number of Alternatives | Algorithm Structure | Ranking | Solution |
---|---|---|---|---|---|
AHP | Large | Limited | Pairwise comparison | Score ranking | Best alternative of all according to criteria and sub-criteria |
ELECTRE | Limited | Limited | Preference thresholds | Preference ranking | Not dominated alternative |
TOPSIS | Large | Large | Ideal solution and negative ideal solution | Score ranking | Alternative closer to the ideal solution and at the same time more distant from the ideal negative solution |
VIKOR | Large | Large | Ideal solution | Score ranking | Alternative closer to the ideal solution |
C1 | C2 | C3 | C41 | C42 | C43 | C5 | |
---|---|---|---|---|---|---|---|
Community Involvement | New Workers | Cultural Effects | Representativeness of the Use Function | Residential Impact | Criterion of Minimum Intervention | ROI | |
[n. users] | [n. workers] | [m2/m2] | [n. users] | [€/€] | |||
A1 | 122 | 14 | 0.335 | 5 | 122 | 3 | 0.073 |
A2 | 168 | 16 | 0.661 | 6 | 168 | 6 | 0.043 |
A3 | 197 | 22 | 0.641 | 6 | 197 | 4 | 0.122 |
A4 | 140 | 16 | 0.205 | 3 | 140 | 5 | 0.101 |
Intensity | 1 | 3 | 5 | 7 | 9 | 2, 4, 6, 8 |
---|---|---|---|---|---|---|
Linguistic | Equal | Moderate | Strong | Demonstrated | Extreme | Intermediate values |
C1–Community Involvement | C1–Community Involvement | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 0.33 | 0.20 | 1.00 | A1 | 0.100 | 0.071 | 0.112 | 0.111 | 0.099 |
A2 | 3.00 | 1.00 | 0.33 | 3.00 | A2 | 0.300 | 0.214 | 0.187 | 0.333 | 0.259 |
A3 | 5.00 | 3.00 | 1.00 | 4.00 | A3 | 0.500 | 0.643 | 0.561 | 0.444 | 0.537 |
A4 | 1.00 | 0.33 | 0.25 | 1.00 | A4 | 0.100 | 0.071 | 0.140 | 0.111 | 0.106 |
CR = 3.80 | CR = 3.80 | |||||||||
C2–New workers | C2–New workers | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 1.00 | 0.20 | 1.00 | A1 | 0.125 | 0.143 | 0.118 | 0.143 | 0.132 |
A2 | 1.00 | 1.00 | 0.25 | 1.00 | A2 | 0.125 | 0.143 | 0.147 | 0.143 | 0.139 |
A3 | 5.00 | 4.00 | 1.00 | 4.00 | A3 | 0.625 | 0.571 | 0.588 | 0.571 | 0.589 |
A4 | 1.00 | 1.00 | 0.25 | 1.00 | A4 | 0.125 | 0.143 | 0.147 | 0.143 | 0.139 |
CR = 0.38 | CR = 0.38 | |||||||||
C3–Cultural effects | C3–Cultural effects | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 0.17 | 0.20 | 3.00 | A1 | 0.081 | 0.073 | 0.085 | 0.158 | 0.099 |
A2 | 6.00 | 1.00 | 1.00 | 8.00 | A2 | 0.486 | 0.436 | 0.427 | 0.421 | 0.443 |
A3 | 5.00 | 1.00 | 1.00 | 7.00 | A3 | 0.405 | 0.436 | 0.427 | 0.368 | 0.409 |
A4 | 0.33 | 0.13 | 0.14 | 1.00 | A4 | 0.027 | 0.055 | 0.061 | 0.053 | 0.049 |
CR = 4.62 | CR = 4.62 | |||||||||
C41—Representativeness of the use function | C41—Representativeness of the use function | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 0.33 | 0.33 | 5.00 | A1 | 0.139 | 0.133 | 0.133 | 0.278 | 0.171 |
A2 | 3.00 | 1.00 | 1.00 | 6.00 | A2 | 0.417 | 0.400 | 0.400 | 0.333 | 0.388 |
A3 | 3.00 | 1.00 | 1.00 | 6.00 | A3 | 0.417 | 0.400 | 0.400 | 0.333 | 0.388 |
A4 | 0.20 | 0.17 | 0.17 | 1.00 | A4 | 0.028 | 0.067 | 0.067 | 0.056 | 0.054 |
CR = 5.28 | CR = 5.28 | |||||||||
C42—Residential impact | C42—Residential impact | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 3.00 | 5.00 | 1.00 | A1 | 0.395 | 0.409 | 0.385 | 0.387 | 0.394 |
A2 | 0.33 | 1.00 | 3.00 | 0.33 | A2 | 0.132 | 0.136 | 0.231 | 0.129 | 0.157 |
A3 | 0.20 | 0.33 | 1.00 | 0.25 | A3 | 0.079 | 0.045 | 0.077 | 0.097 | 0.075 |
A4 | 1.00 | 3.00 | 4.00 | 1.00 | A4 | 0.395 | 0.409 | 0.308 | 0.387 | 0.375 |
CR = 3.16 | CR = 3.16 | |||||||||
C43—Criterion of minimum interventation | C43—Criterion of minimum interventation | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 0.17 | 0.33 | 0.20 | A1 | 0.067 | 0.098 | 0.036 | 0.044 | 0.061 |
A2 | 6.00 | 1.00 | 5.00 | 3.00 | A2 | 0.400 | 0.588 | 0.536 | 0.662 | 0.546 |
A3 | 3.00 | 0.20 | 1.00 | 0.33 | A3 | 0.200 | 0.118 | 0.107 | 0.074 | 0.125 |
A4 | 5.00 | 0.33 | 3.00 | 1.00 | A4 | 0.333 | 0.196 | 0.321 | 0.221 | 0.268 |
CR = 8.26 | CR = 8.26 | |||||||||
C5—ROI | C5—ROI | |||||||||
A1 | A2 | A3 | A4 | A1 | A2 | A3 | A4 | wi | ||
A1 | 1.00 | 3.00 | 0.20 | 0.33 | A1 | 0.107 | 0.188 | 0.119 | 0.074 | 0.122 |
A2 | 0.33 | 1.00 | 0.14 | 0.20 | A2 | 0.036 | 0.063 | 0.085 | 0.044 | 0.057 |
A3 | 5.00 | 7.00 | 1.00 | 3.00 | A3 | 0.536 | 0.438 | 0.597 | 0.662 | 0.558 |
A4 | 3.00 | 5.00 | 0.33 | 1.00 | A4 | 0.321 | 0.313 | 0.199 | 0.221 | 0.263 |
CR = 6.54 | CR = 6.54 |
C1 (Social) | C2 (Cultural) | C3 (Financial) | Priority | |||||
wCi | 0.333 | 0.333 | 0.333 | |||||
C1 | C2 | C3 | C4 | C5 | ||||
wCi | 0.500 | 0.500 | 0.500 | 0.500 | 1.00 | |||
C41 | C42 | C43 | ||||||
wCi | 0.333 | 0.333 | 0.333 | |||||
wA1 | 0.099 | 0.132 | 0.099 | 0.171 | 0.394 | 0.061 | 0.122 | 0.130 |
wA2 | 0.259 | 0.139 | 0.443 | 0.388 | 0.157 | 0.546 | 0.057 | 0.220 |
wA3 | 0.537 | 0.589 | 0.409 | 0.388 | 0.075 | 0.125 | 0.558 | 0.474 |
wA4 | 0.106 | 0.139 | 0.049 | 0.054 | 0.375 | 0.268 | 0.263 | 0.175 |
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Nesticò, A.; Somma, P. Comparative Analysis of Multi-Criteria Methods for the Enhancement of Historical Buildings. Sustainability 2019, 11, 4526. https://doi.org/10.3390/su11174526
Nesticò A, Somma P. Comparative Analysis of Multi-Criteria Methods for the Enhancement of Historical Buildings. Sustainability. 2019; 11(17):4526. https://doi.org/10.3390/su11174526
Chicago/Turabian StyleNesticò, Antonio, and Piera Somma. 2019. "Comparative Analysis of Multi-Criteria Methods for the Enhancement of Historical Buildings" Sustainability 11, no. 17: 4526. https://doi.org/10.3390/su11174526