4.3.2. Multi-Criteria Analysis

Considering the coexistence of different objectives, which have been elicited by the needs and expectations of the actors involved, and by considering values expressed by the BCH, it has been decided to perform an MCA in order to take into consideration this complexity [24]. The decision problem has been structured into four criteria, further divided into sub-criteria. The framework has been developed by both taking into account the final objective of selecting the most sustainable project and combining phases developed during the intelligence phase.

Table 1 presents the value tree defined and there is also information about the nature of the sub-criteria selected.


**Table 1.** Value tree.

Each criterion has been defined regarding the purpose to achieve in order to be satisfied, while for each sub-criterion, a three-part evaluation sheet has been prepared and divided into:


In detail, 1. Functional Sustainability specifically takes into account the characteristics of the structure that will host the territorial health center; in fact, 1.1 Flexibility analyses the ability of the structure to modify its configuration over time according to the needs, therefore the availability of outdoor spaces for future expansions; 1.2 Usability/Accessibility evaluates the easy access to the building by all users, with particular reference to people with disabilities; 1.3 Buffer and common spaces considers the presence of an area in front of the building that allows to facilitate the passage between its interior and exterior area; 1.4 Transformability index is the ability of the structure to modify its internal configuration over time as needed. Then, 2. Socio-cultural Sustainability investigates the functional program of different scenarios; 2.1 Functional mix promotes the coexistence of several functions; 2.2 Social attractiveness is aimed at involving all age groups of the population through the creation of specific functions; 2.3 Aggregation spaces focuses on the creation of open spaces designed to facilitate interaction and living in the open air. Then, 3. Environmental Sustainability considers the external and internal spaces of the territorial health center, with a focus on the design solutions envisaged; 3.1 Harmonization with the context aims at minimizing the interference of the new project with the context; 3.2 Energetic quality evaluates the orientation of the building, the predisposition to accommodate photovoltaic panels and the ratio between the surface and the volume; 3.3 Consistency with constraints takes into consideration the regulations in place in the area. The last criterion, 4. Economic Sustainability, measures the feasibility of the intervention; in fact, 4.1 Construction cost assesses the ex-novo works, the recovery works and the services that will be set up there; 4.2 Maintenance cost considers in a qualitative way the costs for the maintenance of the intervention; 4.3 Profitability of the intervention evaluates the market value generated by different projects.

Given this framework, the alternatives previously generated have been measured and their performances are presented in Table 2 where it is possible to visualize, moreover, the U.M. selected and if the performance has to be maximized (benefit) or minimized (cost).


**Table 2.** Performance matrix.

Notes: + = high; 0 = medium; − = low.

Given the qualitative and quantitative nature of the different sub-criteria and, consequently, the lack of homogeneity of the units of measurement and of the scoring scales, the performances have been standardized with the aim of using the same a-dimensional scale between 0 and 1 for all the values. Consequently, each sub-criterion has been evaluated by means of a specific performance scale appropriate to the object of the evaluation and then standardized in a range from 0 (the worst performance) to 1 (the best performance) in order to be compared synergistically in the final evaluation of the alternatives. The value functions have been discussed with experts with specific knowledge about the procedure to develop during a focus group and it has been decided to use the maximum standardization that means:

$$\text{standard score} = \frac{\text{score}}{\text{highest score}} \tag{1}$$

if the value has to be maximized (benefit), while:

$$stadardized\ score = -\frac{score}{highest\ score} + 1\tag{2}$$

if the value has to be minimized (cost) [25].

The Multi-Criteria Analysis has been carried out with the support of the DEFINITE software (decisions on a finite set of alternatives) [26]. Once the problem has been structured, alternatives measured according to the value tree defined and performances standardized, the next phase, involved in the procedure selected concerns criteria weights elicitation. In order to assign weights to the defined criteria and sub-criteria, one round of questionnaires has been administered to a selected group of experts. In detail, for the criteria, a group of eight experts have been selected, who answered individually to the questionnaire, while for the sub-criteria, only one expert answered for each macro area. The choice of experts has been based on their previous experiences on the proposed topic. The method applied for the weights elicitation has been the point allocation [27]; in fact, the experts have been asked to allocate 100 points among the criteria or sub-criteria proposed, assigning a higher number of points to criteria or sub-criteria with a higher importance. The results of the interaction have been then aggregated in order to obtain a unique weighing (Table 3).


**Table 3.** Weights assigned by experts.

In order to solve the problem, the Multi Attribute Value Theory (MAVT) [28] has been applied. The method allows to handle both qualitative and quantitative data by analyzing a finite set of alternatives [29]. Since there were no specific thresholds to respect, it has been chosen to aggregate standardized scores and weights by the use of an additive method as the MAVT—this means a bad performance is compensated by a good one.

### **5. Results**

Figure 5 shows both the partial results obtained for each criterion and the overall results. The ranking is the result of the weighted sum of the scores of each alternative multiplied by the influence assigned by the experts to criteria and sub-criteria. According to the defined decision framework, the most suitable alternative is Scenario\_3, followed by Scenario\_4, Scenario\_2, Scenario\_1 and Scenario\_0.

**Figure 5.** Partial and Overall results.

By reading the results, it is possible to highlight some considerations:


This result is also confirmed by performing a sensitivity analysis. In fact, Figure 6 shows the results obtained by changing the weights assigned to the four criteria, and four different perspectives are illustrated by the "What if" Scenario.

**Figure 6.** "What if" Scenario

Despite changes in the influence assigned, the rank obtained is stable and robust; in fact, the alternatives maintain the same position. Given the complexity and multi-dimensionality of the decision-making framework, it is important to verify the sensitivity of the result to possible changes.

The sensitivity analysis is a fundamental step in the MCA that is able to improve the quality of the decision and it is a powerful tool when embedded in all the phases of a decision-making process, assigning a higher accuracy to the evaluation [30,31]. In fact, rankings are often conditional, given the uncertainty of data, criteria and also weights, since DMs are not always aware about their preferences. In particular, when multiple stakeholders are involved, it is difficult to select the best procedure to aggregate their weights and to elicit them [32,33]. The role of the sensitivity analysis is strategic in this context for the validation of the output and to reduce the uncertainty.

According to the results obtained, further confirmed by the sensitivity analysis, and trying to provide an answer to the research question stated in the introduction, it is possible to underline the following remarks:


### **6. Conclusions**

The methodology proposed aimed at supporting the DM in the selection of the most suitable scenario for an urban regeneration that involves the location of a territorial health center and the enhancement of the BCH. One of the main focuses of the contribution has been to present a multi-methodological approach and to explain each phase by illustrating how it has been developed. In fact, when multiple stakeholders are involved, multiple and sometimes conflicting values and expectations are at stake and it is fundamental to understand which are the most urgent to satisfy. At the same time, when the process of regeneration embeds tangible cultural values and intangible values, the support of a robust method able to elicit them and to recognize which have to be maximized or implemented and which are the most critical becomes strategic. In fact, both the approaches stated in the intelligence phase, together with the analysis of existing case studies, are functional to the generation of alternatives. These are the results of a strict cooperation with the actors involved and of a strict comprehension of values carried on by the BCH. Moreover, the combination of the DCF Analysis with the MCA for the evaluation of alternatives, given their transparency and robust methods, supports the DM in understanding the feasibility of the projects with their strengths and weaknesses. The final decision is, moreover, enhanced by the sensitivity analysis able to validate the results obtained.

The methodology and the approach proposed, if applied appropriately, could moreover facilitate the interaction and the satisfaction of both public and private parties and improve the policy-making process. In fact, since it is supported by evidence, it could lead to the concept of Evidence-Based Policy Making, where the consensus about policies is obtained through evidences [34]. Following this idea and by the active participation of many different actors, the DM is even more justified in taking a final decision. The policy implication becomes fundamental considering the context of application described in this paper since the location of a territorial health center is also evaluated. This public service is aimed at serving the population and, in the current scenario of increasing urbanization, health facilities play an important role as urban elements that can trigger and stimulate benefits throughout the territory [35]. Their location can also strongly affect the success of the whole project and may have negative impacts in several respects, such as patient well-being and the service's efficiency [36].

The methodology is able to consider all the aspects recognized as urgent to investigate and could facilitate the whole decision process, contributing to the literature on soft OR and covering all the four different approaches aimed at enhancing the cultural heritage and able to support city regeneration described in the introduction. Moreover, this first attempt could be investigated and different MCA approaches can be explored in order to better understand which is the most suitable one in this context. For example, if the DM has a deeper knowledge of the project and owns more information, it could be possible to test the aggregation by defining thresholds of acceptability (partially compensatory or non-compensatory methods) or by applying other additive models. In addition, the topic regarding the possible uses of historical buildings could be facilitated by exploring the methodology proposed by [37].

Given these conclusions, it is possible to perceive the flexibility of the methodology proposed and the iterative nature of the process. In fact, according to the case study, to the context of application and to the stakeholders involved and their values, a different path can be processed considering the general framework previously shaped.

**Author Contributions:** Conceptualization, S.C.; Data curation, R.M.; Formal analysis, L.S.; Methodology, M.D.; Project administration, R.M.; Supervision, S.C. and S.D.T.; Validation, S.D.T.; Visualization, M.D.; Writing—original draft, M.D.; Writing—review and editing, S.C., L.S., R.M. and S.D.T.

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

**Acknowledgments:** This study was partially supported by the Municipality of Vimercate (MB), Italy, for which the authors are most grateful.

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