**4. Selection of the Best Use of a Historic Building. Characterization of a Hierarchical Analysis Model**

The Analytic Hierarchy Process is defined as "analytical" because it breaks down the complex decision problem into fundamental constituent elements [30,31,41,42]; "hierarchical" because the breakdown of the problem itself occurs at successive levels characterized by ever-increasing detail [27,28,43,44]. At the top of the hierarchy, there is the goal to be reached, which, in the case under consideration, is given by the best use for the historic building.

The choice of indicators is fundamental for the correct application of the model. Here, they have been selected from literature datasets [45–48].

At the first level, we consider the social (*C1*), cultural (*C2*), and financial (*C3*) criteria, which are described in turn in the sub-criteria. In particular, the social criterion includes the sub-criteria:


The financial criterion includes the sub-criterion:


According to the existing technical-urban planning constraints and in relation to the socio-demographic and economic characteristics of the territory in which the recovery and enhancement project of the historic building is inserted, the analysts define the possible investment alternatives *A*1, *A*2, ..., *An*. Among these, it is necessary to make the choice that guarantees the optimal use, according to the multiple criteria *C1*, *C2*, *C3* and sub-criteria *C*1, *C*2, *C*3, *C*4, *C*5, as well as *C*41, *C*42, and *C*<sup>43</sup> defined above. The logical-operative scheme outlined finds graphic representation in Figure 1.

**Figure 1.** Hierarchical structure of the proposed model.

### **5. Case Study and Results**

The aim of the paper was to define the best use for the recovery and enhancement of a former convent in the province of Salerno (Italy). For this purpose, in accordance with the provisions of paragraph 3, the Analogue Hierarchy Process was used. This is a multi-criteria approach able to take into account both the use value of cultural heritage as a source of economic growth in the short term, and its intrinsic value as an identity element of a community, to be preserved in the long term [51].

The monastic complex under study is of particular historical-architectural interest, but is currently in a very poor state of preservation. Thus, the public administration acquired the property with the aim of recovering it [52–55]. Figure 2 shows the plants, sections, and main elevations of the building in the actual state.

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**Figure 2.** Former convent in the province of Salerno (Italy): (**A**). plans; (**B**). sections; (**C**). elevations.

Depending on the technical-urban planning constraints and the economic characteristics of the area in which the historic building is located, possible uses are:



The Figures A1–A12 in the Appendix A report the functional distribution of the internal spaces at the three levels of the building for each of the four solutions of use.

The AHP was developed according to the first-level evaluation criteria: social (*C*1), cultural (*C*2), and financial (*C*3). For the case in question, the sub-criteria are estimated as follows:


Once the alternatives, criteria, and sub-criteria for the evaluation was defined, the hierarchical decision model was outlined, as shown in Figure 3.

**Figure 3.** The hierarchical structure for the case study.

Table 3 shows the scalarized decision matrix, useful for the implementation of the AHP. In this matrix the generic element *aij* (attribute) expresses the performance of the generic alternative *Ai* (*i* = 1, 2, ..., *n*) with respect to the generic criterion *Cj* (*j* = 1, 2, ..., *m*) [56,57].


**Table 3.** Scalarized decision matrix.

The dominance coefficients were assigned according to Saaty's semantic scale in Table 4. They are representative of the relative importance between the compared elements [33].



In paired comparisons of the alternatives with respect to the criteria, graduated scales were used, each divided into equal bands corresponding to the intensity of the Saaty scale, where the maximum value of the indicator in question corresponds to the upper end. On the scale thus defined, the numerical values of the indicators have been positioned for each alternative (Figure 4). If there is only one band between the indicators, then the strongest value was given coefficient 3, and to the other, the reciprocal; if there are two bands, the strongest value was assigned coefficient 5, and to the other, the reciprocal, and so on. In intermediate situations, there were intermediate intensities.

**Figure 4.** Scales for determining the dominance coefficients.

Table 5 contains the matrices of pairwise comparisons and the matrices of normalized pair comparisons. From these matrices, processed by implementing Microsoft Excel software, it was possible to obtain the weights of each alternative with respect to each sub-criterion. In all cases, the matrices are consistent. In fact, being of rank 4, they have a value of consistency ratio lower than 9.


**Table 5.** Comparison matrices in pairs between the alternatives with respect to each criterion.

In the preparation of the matrices of pairwise comparisons, both between criteria and between sub-criteria, we assigned equal weight to each criterion, and with reference to the single criterion, we assigned the same weight to each sub-criterion. All matrices were consistent.

The total priorities are shown in Table 6. The AHP therefore identifies the local cuisine restaurant as the best destination for the recovery and enhancement of the former convent.


**Table 6.** Priority matrix.

### **6. Discussion**

The selection of possible alternatives of use for the historical building under study was derived from a careful analysis of the needs of citizenship, and from the economic and socio-demographic characteristics of the reference territory. In particular, the choice of the B&B was born from the need to improve the reception services connected to the use of the existing historical, architectural, and archaeological heritage. The multi-purpose hall option was aimed at the cultural growth of the city, which was also poorly equipped with facilities for conferences, seminars, and professional training. The local cuisine restaurant destination with its museum of rural civilization intends to recover the building as the driving force of an economy capable of enhancing the typical local products, as in the past, the convent—thanks to the presence of Benedictine monks—was a point of reference for the agricultural development of a marginal area. The office function can allow the urban center to play a central economic role.

Table 5 of the priorities shows that, due to the multiple evaluation criteria considered, the AHP method considers *A*<sup>3</sup> as the best alternative. Thus, the optimal use is that of the local cuisine restaurant, with a score of 0.474. In the order of the alternatives: *A*<sup>2</sup> (multi-purpose rooms) with a score of 0.220, that is less than half of the valid score for the first solution in the ranking; *A*<sup>4</sup> (offices) with a score of 0.175; and *A*<sup>1</sup> (bed & breakfast) with a score of 0.130.

### **7. Conclusions**

Historical environments are an exhaustible resource, so it requires great attention in terms of protection, but also of enhancement. This can happen through the functional recovery of the building with the identification of its best use, intended as a function able to simultaneously maximize the social, cultural, and financial effects that the intervention on the historic building generates on the reference territory. This approach respects the principles of sustainable urban development.

The aim of the research is to outline a multi-criteria evaluation model able to select the optimal function for a historic building in a state of neglect. From this point of view, a comparative analysis was carried out on some of the most well-known Multi-Criteria Decision Making methods: the Analitic Hierarchy Process (AHP), ELimination Et Choix Traduisant la REalité (ELECTRE), Tecnique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the Compromise Ranking Method (VIKOR). The theoretical examination highlights that, due to its hierarchical structure, the AHP model allows the

problem to be broken down to the level of detail necessary for the analysis, thus being more effective in solving the problem in question, where, very often, there are multiple criteria and sub-criteria of evaluation.

For the correct implementation of the hierarchical analysis algorithms, the rigorous selection of the evaluation criteria and sub-criteria, as well as the corresponding indicators, is fundamental. This selection represents an element of novelty of the research. The study led us to recognize: the social criteria, which can be expressed through the community involvement and the new workers; cultural criteria, translated in terms of cultural effects and compatibility of the function with the historical-architectural characteristics of the property; and financial criteria, to be expressed quantitatively by the Return On Investment. It should be noted that a careful study on the compatibility of the function with the historical-architectural characteristics of the property leads to a breaking down of this criterion into the three interventions.

The operational coherence of the evaluation model is verified through a case study, concerning the selection of the optimal destination for a former convent in the province of Salerno (Italy).

The multi-criteria analysis model proved to be an effective decision support tool, guaranteeing to both public administrations and private individuals an optimal allocation of available resources, with obvious and important implications of economic policy.

**Author Contributions:** Conceptualization, A.N.; Data curation, A.N and P.S.; Formal analysis, A.N. and P.S.; Methodology, A.N. and P.S.; Software, A.N. and P.S.; Supervision, A.N.; Validation, A.N.; Writing—original draft, A.N. and P.S.; Writing—review & editing, A.N.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflicts of interest.

## **Appendix A**

**Figure A1.** B&B ground floor plan.

**Figure A2.** B&B first floor plan.

**Figure A3.** B&B attic floor plan.

**Figure A4.** Multi-purpose rooms ground floor plan.

**Figure A5.** Multi-purpose rooms first floor plan.

**Figure A6.** Multi-purpose rooms attic floor plan.

**Figure A7.** Local cuisine restaurant ground floor plan.

**Figure A8.** Local cuisine restaurant first floor plan.

**Figure A9.** Local cuisine restaurant attic floor plan.

**Figure A10.** Offices' ground floor plan.

**Figure A11.** Offices' first floor plan.

**Figure A12.** Offices' attic floor plan.

### **References**


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