**4. Model Calibration and Results**

The calibration of the model Ahp2 was carried out verifying the congruence of the ranking of the villas with known economic use (three villas managed by the Fondazione Ville Vesuviane: Villa Campolieto, Villa Ruggiero and Villa Favorita); more specifically, comparing the rankings obtained by models Ahp1 and Ahp2, or also comparing vector *u* with vector *v*.

The results show that all the villas have a good level of economic vocation. The economic vocation model so validated is thus applied to the five villas of the case study. The results are in Figures 9 and 10.



**Figure 10.** Calibration phase: Overall synthesized priorities for the alternatives (Model Ahp2).

It is clear that the best potentials are those of Villa Durante with the value 0.866 (see Figure 11), and then Villa Giulio de la Ville (0.779), Villa Arena (0.721), Villa Lucia (0.660) and Villa Manes Rossi (0.650).

However, when trying to evaluate individual clusters of indicators, the final situation is different.


**Figure 11.** Results: Overall synthesized priorities for the alternatives (Model Ahp2).

Analyzing only the characteristics about the villa's localization (CLO) the results are shown in Figure 12.

The highest value is still that of Villa Durante, but the other values are changed, and also the order of the villas.


**Figure 12.** Overall synthesized priorities for the alternatives from the network characteristics about the villa's localization (CLO) (Model Ahp2).

We continue the verification with the other two categories of indicators, CLE (characteristics about the ownership and legal structure, see Figure 13) and CIN (intrinsic characteristics of the villa, see Figure 14), and the results change each time.


**Figure 13.** Overall synthesized priorities for the alternatives from the network CLE (Model Ahp2).

The valuations highlight the more relevant indicators for the definition of the vocationality of the properties object to study: The aesthetic value, the presence of external areas and the more or less fractioned ownership regime undoubtedly have a very important weight.


**Figure 14.** Overall synthesized priorities for the alternatives from the network intrinsic characteristics of the villa (CIN) (Model Ahp2).

Finally, it is possible to evaluate how strong an alternative choice for the calculation of vocationality is through a sensitivity analysis (see Figures 15–17).

**Figure 15.** Sensitivity analysis based on the CIN criteria (intrinsic characteristics).

The diagram with colored bars in the table shows how the results of vocationality change when trying to modify the values of the CIN by 50% (see Figure 15). Following are similar examples but with variation in CLO (see Figure 16) and CLE criteria (see Figure 17).

**Figure 16.** Sensitivity analysis based on the CLE criteria (characteristics about the ownership and legal structure).

**Figure 17.** Sensitivity analysis based on the CLO criteria (characteristics of localization).

### **5. Conclusions**

The Vesuvian Villas, although a few are different from a functional and structural point of view, have unfortunately undergone several changes over time. Many of these villas are still used as homes today, but the original functional relationship between agricultural production and country residence has gone down (see Figure 18). This is due, in particular, to the poor profitability of the buildings and the division of properties, which, over time, have caused the alienation of soils and the worsening of environmental conditions. No villa performs the function for which it was built; most of them are used as a rustic house, warehouse, restaurant or, at best, in a converted house or museum.

**Figure 18.** G. Carafa, Duke of Noja. Ancient topographic map of Naples and its hinterlands (1775), particularly of the "Strada Regia delle Calabrie".

In any case, they remain identity assets that connote geographic spaces and represent an inalienable patrimony of historical, environmental and artistic values to be protected and enhanced, since they nourish the identity of a community and guarantee a historical and cultural continuity.

The study proposes a model of analysis and evaluation of the vocationality of historical–architectural buildings in order to assess economic uses compatible with the needs of protection and conservation. Despite the evidence of these potentialities, the difficulties to convert qualitative variables into quantitative algorithms are a complex issue. These difficulties were particularly evident in the construction of the hierarchical model for the evaluation of vocationality. A further objective difficulty is the substantial absence of consolidated models of conservative economic re-use to be considered for the calibration of the potential vocationality. Not to underestimate, then, the usual and chronic lack of economic information: On the one hand, there are widely available information about historical and architectural aspects of the buildings, as well as their state of maintenance; on the other hand, there is total lack of information on the forms of buildings management and their consequent economic results [18–20]. This gap is only partially filled through the use of indirect indicators, such as revenue, grade and type of use. Only recently, due to high maintenance costs, the owners of the Vesuvian Villas have begun to consider economic use as a possible alternative to abandonment and, in this sense, the initiatives remain rather limited and still in the start-up phase. Therefore, the analysis carried out is a first attempt at reading a particularly changeable and unstable reality, where the use of the architectural artefact appears to be poised between distortive transformations (such as the intensive residential destination in peripheral urban areas) and recovery to original function as prestigious

residence converted for public uses (libraries, corporate offices, museums, etc.). The applied model has demonstrated a good ability to identify the most favored realities to accommodate the forms of use compatible with conservation, also thanks to the possibility offered by the hierarchical analysis to build very articulated models, and being able to capture and incorporate into the evaluation more different aspects. Further model developments may be based on an improvement in the quality and quantity of economic data, in order to improve the fitting of the model. Evaluating the vocationality in relation to different forms of economic use can therefore provide useful indications to operate stratifications on the heritage of the Vesuvian Villas, in order to suggest private management strategies for individual assets; support the formation of adequate protection policies; and, last but not least, improve the efficiency of the few public funds available for the protection of a heritage unique for consistency and historical–architectural relevance.

**Author Contributions:** The paper is attributed in equal part to all authors. All authors have read and agreed to the published version of the manuscript.

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

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