People and the City: Urban Fragility and the Real Estate-Scape in a Neighborhood of Catania, Italy

: Urban / social fragility is the main focus of most studies on civil economy involving the commitment of politics in the prospect of integrating and somehow guiding an ordered development of and ordered communities. The contemporary city is strongly inﬂuenced by the incommunicability between the social system and environment, the latter more and more, including urban and societal components. This study tries to outline a comparative social-urban proﬁle of Picanello, a popular central neighborhood of Catania, in Sicily, Italy, characterized by the combination of di ﬀ erent urban and social life-quality levels, thus expressing a heterogeneous vulnerability / resilience proﬁle. The analysis is placed in the urban planning context and aims to: (1) Denotative a pattern that considers the di ﬀ erent fragility / resilience descriptive indices; and (2) connotative a pattern of the human and urban dimensions of the social capital asset. This analysis was performed by implementing a multidimensional pattern allowing us to place the neighborhood in a ranking of the neighborhoods of Catania, thus highlighting strength and weakness under di ﬀ erent respects. Furthermore, the monetary measurements of this vulnerability / resilience proﬁle, was carried by means of the structured observation of the real estate market. Fuzzy k-medoids cluster analyses have been comparatively performed—showing and mapping the relationships between urban value density and real estate market prices tensions.


Fragility and the City. General Premises for a Definition of "Real Estate-Scape"
Urban fragility is one of the big issues that faces late-modern cities who are committed to cope with the growing external pressures (from the environment) and internal tensions (within the social system)-referable to the socio-cultural and political-economic climate, in the current "Age of Changes". This issue is placed in a very wide institutional context [1], where studies and reports have shown how this criticality is linked above all to the growing complexity of the cities [2,3]. The increase in population, extension, and density, the growing cultural mixite, the fast "filtering up and down" processes, are some symptoms of the combination of two fundamental drivers. Firstly, the exponential technological progress-mostly concerning the geographical and digital accessibility-has been encouraging far more people to claim a better socio-economic status, which urban location is a symbol of. Secondly, the progressive human/environmental unfairness of economy over the planet and the related increase in insecurity, push the transfer of large masses of the population towards the 1.
On the one hand, by internal production of entropy, whose higher rate is due to the greater urban vitality and vibrancy [18]; 2.
On the other hand, by incoming/outgoing fluxes of entropy [19] whose higher rate is due to the greater capacity by the administrative system to manage the system-environment exchanges, thus replacing the production of entropy (the natural disorder from inside), with fluxes of neg-entropy (the artificial order form outside) [20].
The thermodynamic synecdoche can reverse the semantic relationship in the metaphors of diffusion and viscosity. In general: The lower entropy, the lower the social-economic-cultural exchanges and wealth production, as well as pollution, urban sprawl, and land consumption, and vice versa. The synthesis of this contradiction is the sustainable development based on immaterial production/consumption patterns and high-information content circular economy [21,22].
In the field of urban fragility, the ambiguity of this thermodynamic synecdoche depends on the possible points of view. In the case of an environmental pressure (physical catastrophe or economic crisis) viscosity (in the aforesaid social-communicative meaning) could affect the diffusion of the material and public economic support (from Civil Protection and Welfare) whose thermodynamic synecdoche is the energy; by definition, energy is not a value in itself but only if it is possible to regulate its accumulation, releasing, allocation and recycling.
Both in the ordinary and emergency conditions, such a normative pattern is generally implemented through the bureaucracy that, in turn, might increase viscosity, as in the cases of the recent reconstruction programming in the center-Italy areas affected by the earthquake, as well as in the current economic planetary crisis from the Covid-19 pandemic.
Specifically, in the field of urban redevelopment programs, viscosity could concern the characteristics of the load-bearing masonry buildings. In a negative sense, these characteristics reduce the flexibility of the requested uses and the adaptation of the buildings to contemporary needs typically due to the evolution of the size and composition of the households; considered positively, this viscosity contains the spread of renovations potentially harmful to the identity of historic neighborhoods. In sum, the socio-economic context makes ambiguous the interpretation of the indices usually assumed for outlining the profile of vulnerability in a social and urban sense; the real estate market analysis can contribute to enrich the vulnerability concept and disambiguate such misinterpretations.

Urban Fragility. Some Literature Coordinates
Fragility is a wide concept [23] connecting several epistemic areas and enabling different cognitive functions, respectively ranging from natural to cultural topics, as well as from individual to social spheres, and above all, supporting the public decision-making [24,25], in the prospect of the best connection between the certainty of present and the uncertainty of future. Fragility, as specified in the multiple operating contexts of vulnerability, is the most committing area for the exercise of the social, political, and economic accountability [26][27][28].
The common denominator of the multiple definitions of vulnerability is risk; risk, in turn, is the expectation of a sudden environmental fluctuation, that affects a defined social system [29,30] in the extent it stops, or significantly reduces, its ability to fulfil the core functions in the long run, and to recover the previous status in the short-medium run.
According to the afore outlined communicative-cognitive approach to the relationship between the (social) system and (natural, artificial, and human) environment, risk should be considered as external by definition, in so far as it comes from the environment. As a result, vulnerability and resilience are internal characteristics of the system. Accordingly, if resilience is the ability of the social system to cope with external risk, social capital is the strategic variable for analysis, valuation and decision making [31] that identify-basing on relevant and accessible data-fragility and resilience factors at the city level: Rapid and unregulated urbanization; income and social inequality; concentrated poverty; unemployment; policing and justice deficits; real and perceived insecurity; exposure to natural hazards, such as droughts, cyclones and floods [13,[32][33][34][35][36][37][38][39][40]. Symmetrically, resilience factors are assumed: Higher income and social equality; effective policing and judicial mechanisms; micro-economic security and social protection; the provision of basic services; social cohesion; social networks and social support; strong community to government and inter-governmental cooperation [41,42].
Miklos and Paoliello [43] highlighted inequality as the main driver of urban fragility thus confirming that a sociological approach cannot do without an ethical concern calling in question the cognitive and operative category of capital assets, as the topical watershed between social inclusion and exclusion [44].
This study aims at finding some of these topics with reference to Picanello, a popular neighborhood of Catania, Italy, trying: 1.
To outline a comparative social-urban profile of the neighborhood, characterized by the combination of different urban and social life-quality levels, and expressing a heterogeneous vulnerability/resilience profile, compared to the whole urban context of the city of Catania.

2.
To refer this vulnerability/resilience profile to the abstract monetary measurement of the housing market price, thus assuming the real estate-scape as the more general and explicit form of the urban and human scape. Such monetary measurement, in fact, can be considered explicit and significant because real estate capital asset is one of the main items of the household budget for both owners and tenants. Accordingly, a real estate survey and a structured cluster analysis have been carried out to highlight the quantitative and spatial relationships between social-material vulnerability/resilience indices and real estate capital asset market prices. A further hypothesis is that real estate capital asset is a sort of stock-value accumulator that prevents urban-human-scape from being affected by sudden economic fluctuations, such as the recent economic-financial crisis. The analysis, placed in the urban planning context, intends to provide, as first, a denotative pattern taking into account different fragility/resilience descriptive indices coming from different data-sources, specifically selected in order to connotate the human and urban dimensions of the social capital asset. This analysis was performed by implementing a multidimensional pattern [45] allowing us to place Picanello neighborhood in a ranking of the neighborhoods of Catania, thus, highlighting strengths and weaknesses under different respects. As second, a typical connotative analysis, concerning the monetary measurements [46] of this vulnerability/resilience profile [47] was carried out by means of a real estate market survey. This analysis tries to detect and map over the neighborhood area, the economic layout of this profile, enriching the overall qualitative measurements involving the whole neighborhood, with point analyses mapping the heterogeneity of this multifaceted urban area. Fuzzy k-medoids cluster analyses have been comparatively performed, showing the relationships between urban value density and real estate market prices tensions.

Materials: Picanello Neighborhood and the City of Catania
The area nowadays occupied by the neighborhood of Picanello (Figure 1a) is one of the two expansion zones, namely, the north-eastern one, of the historic urban core of Catania. The district is part of the "historic periphery" extending beyond the "Cinda daziaria" (duty walls) in 1895 ( Figure 1b). The area was intended to this purpose starting from the end of XIX century within the Masterplan drafted between 1879 and 1882 by F. Fichera and B. Gentile Cusa. In that period the municipality started to deal, although unsuccessfully, both the poor housing condition compared to the new standards, and the disordered and episodic new buildings in the countryside.
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 38 neighborhood area, the economic layout of this profile, enriching the overall qualitative measurements involving the whole neighborhood, with point analyses mapping the heterogeneity of this multifaceted urban area. Fuzzy k-medoids cluster analyses have been comparatively performed, showing the relationships between urban value density and real estate market prices tensions.

Materials: Picanello Neighborhood and the City of Catania
The area nowadays occupied by the neighborhood of Picanello ( Figure 1a) is one of the two expansion zones, namely, the north-eastern one, of the historic urban core of Catania. The district is part of the "historic periphery" extending beyond the "Cinda daziaria" (duty walls) in 1895 ( Figure  1b). The area was intended to this purpose starting from the end of XIX century within the Masterplan drafted between 1879 and 1882 by F. Fichera and B. Gentile Cusa. In that period the municipality started to deal, although unsuccessfully, both the poor housing condition compared to the new standards, and the disordered and episodic new buildings in the countryside. Even the Masterplan of 1934 could not start the construction of the neighborhood, due to the incompleteness of the administrative process covering just the zoning plan, then further updated, in 1952, when, finally, the municipal administration established the municipal delegations for decentralizing the utilities in the new suburbs. According to the Masterplan by Piccinato, in 1964, a Directional and Commercial Centre was supposed to be constructed in Picanello (Figure 2, zone "I" in fuchsia), after the preparation of a Detailed Plan, thus supporting the creation of a new urban pole. Even the Masterplan of 1934 could not start the construction of the neighborhood, due to the incompleteness of the administrative process covering just the zoning plan, then further updated, in 1952, when, finally, the municipal administration established the municipal delegations for decentralizing the utilities in the new suburbs. According to the Masterplan by Piccinato, in 1964, a Directional and Commercial Centre was supposed to be constructed in Picanello (Figure 2, zone "I" in fuchsia), after the preparation of a Detailed Plan, thus supporting the creation of a new urban pole.  As for ACE 12, Picanello is the most populous municipal area of Catania (14,438 inhabitants; 17,980 inhabitants/sq.km) and one of the most densely built (Figure 4).    As for ACE 12, Picanello is the most populous municipal area of Catania (14,438 inhabitants; 17,980 inhabitants/sq.km) and one of the most densely built (Figure 4).  As for ACE 12, Picanello is the most populous municipal area of Catania (14,438 inhabitants; 17,980 inhabitants/sq.km) and one of the most densely built (Figure 4).  The urban-scape characterized by an urban fabric, including a wide range of building types, also due to the recent replacement of the original buildings by the contemporary ones and public facilities, sometimes strongly modifying the original settlement arrangement ( Figure 5). Many social and urban criticalities affect the neighborhood whose complexity and contradictions compensate to each other, thus revealing a significant degree of vitality, as well as outlining positive prospects and opportunities. The urban-scape characterized by an urban fabric, including a wide range of building types, also due to the recent replacement of the original buildings by the contemporary ones and public facilities, sometimes strongly modifying the original settlement arrangement ( Figure 5).  The urban-scape characterized by an urban fabric, including a wide range of building types, also due to the recent replacement of the original buildings by the contemporary ones and public facilities, sometimes strongly modifying the original settlement arrangement ( Figure 5). Many social and urban criticalities affect the neighborhood whose complexity and contradictions compensate to each other, thus revealing a significant degree of vitality, as well as outlining positive prospects and opportunities. Many social and urban criticalities affect the neighborhood whose complexity and contradictions compensate to each other, thus revealing a significant degree of vitality, as well as outlining positive prospects and opportunities.

Methods
The paper aims at providing some measurements of fragility and resilience of the neighborhood of Picanello, in the more general context of the city of Catania, with reference to the concepts of "human capital" and "urban capital" (Figure 6). With the purpose of providing a comparison of the different urban districts, a multidimensional qualitative assessment pattern was implemented using indices coming from different sources, mainly from the National Institute of Statistics. Specifically, as for the urban capital, due to the specific focus on social issues, we carried out a further study concerning the real estate-scape by means of a housing market survey involving a significant sample of properties over the neighborhoods, as well as samples of similar properties over the whole municipal territory, one for each neighborhood. Further information comes from the Observatory of the Italian Property Market of the National Revenue Agency providing the reference (minimum, average and maximum) unit prices and rent by micro-area of each municipality over the whole national territory.

Methods
The paper aims at providing some measurements of fragility and resilience of the neighborhood of Picanello, in the more general context of the city of Catania, with reference to the concepts of "human capital" and "urban capital" (Figure 6). With the purpose of providing a comparison of the different urban districts, a multidimensional qualitative assessment pattern was implemented using indices coming from different sources, mainly from the National Institute of Statistics. Specifically, as for the urban capital, due to the specific focus on social issues, we carried out a further study concerning the real estate-scape by means of a housing market survey involving a significant sample of properties over the neighborhoods, as well as samples of similar properties over the whole municipal territory, one for each neighborhood. Further information comes from the Observatory of the Italian Property Market of the National Revenue Agency providing the reference (minimum, average and maximum) unit prices and rent by micro-area of each municipality over the whole national territory. To compare and combine quantities available over different scales and expressed in various units of measurement, the indices have been normalized on a standard scale. To do so, according to the specific indices, we assumed benchmarks from the same city, from other Sicilian cities or, in some cases from other Italian cities, if recognized as more appropriate.

The Overall Multidimensional Qualitative Pattern
The general qualitative model performs the approach based on the Multiple Attribute Utility Theory (MAUT) method [50,51] since no decision-making process needs to be carried out in the present experiment.
The basic idea is that a single action (in this case a neighborhood) is differently worth under multiple respects (criteria), which can be furthermore differently relevant or significant to the scope of the assessment. This relevance can be represented by a weight measuring the relative importance of each criterion in respect to the others.  To compare and combine quantities available over different scales and expressed in various units of measurement, the indices have been normalized on a standard scale. To do so, according to the specific indices, we assumed benchmarks from the same city, from other Sicilian cities or, in some cases from other Italian cities, if recognized as more appropriate.

The Overall Multidimensional Qualitative Pattern
The general qualitative model performs the approach based on the Multiple Attribute Utility Theory (MAUT) method [49,50] since no decision-making process needs to be carried out in the present experiment.
The basic idea is that a single action (in this case a neighborhood) is differently worth under multiple respects (criteria), which can be furthermore differently relevant or significant to the scope of the assessment. This relevance can be represented by a weight measuring the relative importance of each criterion in respect to the others. Table 1 displays the general pattern for the outranking of n actions according to m criteria: Table 1. General representation of a multicriteria ranking problem. Weights Where a i is the generic action (neighborhood); x j is the generic main criterion representing a significant issue of fragility/resilience of the neighborhood in terms of social capital); k ij is the assessment of the i th action from the perspective of the j th criterion; λ j is the weight of the j th criterion.
An early approach to the global comparative assessment V i is the weighted average of the k ij : under the hypothesis: The complexity of the actions to be assessed and compared suggest creating a pattern connecting the different values that have been recognized as relevant to measure and compare the different neighborhoods to each other.
The elementary scores k ij , in turn, come from a structured set of sub-scores arranged according to a hierarchic dendrogram rooting to the human and urban dimensions of the social capital ( Table 2, Appendix A). The synthetic pattern is the following: The sub-scores are attributed to the entries placed in the final level of the dendrogram and calculated because of the normalization, described above, over a 0-2 range (Figures 6 and 7). Each of the six last graphs reports two indicators, and consequently, two dots.

Housing Market of Picanello and Overall Urban Real Estate-Scape References
As aforementioned, due to the specific focus on the social issue, the housing market survey concerned two different dimensions, the urban one, with a sample of 72 properties, and the neighborhood one, with a sample of 81 properties of which asking prices are reported as the number of rooms and sq.m. (Figure 8). (titles of the graphs), on the ordinate the normalized score. (b) Utility functions for some significant fragility/resilience indices of urban capital. The red dot represents the value of the index and the score for Picanello. On the abscissa the indicator (titles of the graphs), on the ordinate the normalized score. Each of the six last graphs reports two indicators, and consequently, two dots.

Housing Market of Picanello and Overall Urban Real Estate-Scape References
As aforementioned, due to the specific focus on the social issue, the housing market survey concerned two different dimensions, the urban one, with a sample of 72 properties, and the neighborhood one, with a sample of 81 properties of which asking prices are reported as the number of rooms and sq.m. (Figure 8). 1 general location characteristics, 2 : micro-environmental functional and symbolic features, intrinsic characteristics (such as panoramic quality; view; brightness; lift; security; etc.), , technology, and 1 building architectural quality, and 2: architectural property quality.
The elements of the sample have been scored from the point of view of each elementary subcharacteristic and, by aggregating them by the main characteristics they belong to, each element is characterized by six aggregated scores ranging from 1 (poor quality) to 5 (excellent quality). Finally, at the ultimate level of abstraction of the concrete qualitative values, a further aggregation of the six scores into one, * , provided synthetic information about the general relationship between urbanhuman value and unit prices ( Figure 9). The properties are characterized by six primary qualitative characteristics, articulated in 17 sub-characteristics. The main are: ke1 general location characteristics, ke2: micro-environmental functional and symbolic features, ki intrinsic characteristics (such as panoramic quality; view; brightness; lift; security; etc.), kt, technology, and ka1 building architectural quality, and ka2: architectural property quality.
The elements of the sample have been scored from the point of view of each elementary sub-characteristic and, by aggregating them by the main characteristics they belong to, each element is characterized by six aggregated scores ranging from 1 (poor quality) to 5 (excellent quality). Finally, at the ultimate level of abstraction of the concrete qualitative values, a further aggregation of the six scores into one, k * , provided synthetic information about the general relationship between urban-human value and unit prices ( Figure 9). (titles of the graphs), on the ordinate the normalized score. (b) Utility functions for some significant fragility/resilience indices of urban capital. The red dot represents the value of the index and the score for Picanello. On the abscissa the indicator (titles of the graphs), on the ordinate the normalized score. Each of the six last graphs reports two indicators, and consequently, two dots.

Housing Market of Picanello and Overall Urban Real Estate-Scape References
As aforementioned, due to the specific focus on the social issue, the housing market survey concerned two different dimensions, the urban one, with a sample of 72 properties, and the neighborhood one, with a sample of 81 properties of which asking prices are reported as the number of rooms and sq.m. (Figure 8). 1 general location characteristics, 2 : micro-environmental functional and symbolic features, intrinsic characteristics (such as panoramic quality; view; brightness; lift; security; etc.), , technology, and 1 building architectural quality, and 2: architectural property quality.
The elements of the sample have been scored from the point of view of each elementary subcharacteristic and, by aggregating them by the main characteristics they belong to, each element is characterized by six aggregated scores ranging from 1 (poor quality) to 5 (excellent quality). Finally, at the ultimate level of abstraction of the concrete qualitative values, a further aggregation of the six scores into one, * , provided synthetic information about the general relationship between urbanhuman value and unit prices ( Figure 9). This early analysis provides some references for the next comparisons of housing market prices of Picanello to the other neighborhoods, as well as the following representation of the marginal unit prices, i.e., the ratios between the unit prices and the aggregate score k * , represented in similar graphs ( Figure 10 This early analysis provides some references for the next comparisons of housing market prices of Picanello to the other neighborhoods, as well as the following representation of the marginal unit prices, i.e., the ratios between the unit prices and the aggregate score * , represented in similar graphs ( Figure 10): The varied combination of vulnerability and resilience factors affecting the several components of the human and urban capital reflected in these particular "real estate-scape" results in a variety of situations in which these values interact: Sometimes they compensate and somehow neutralize to each other; otherwise, they accumulate, affecting the expected price both upward and downward.
The approximation of this early analysis, as well as the wide dispersion of the scatter over the trend line and the low coefficient of determination, suggest carrying out a further study. The latter measure and maps the real estate-scape of the neighborhood in order to outline its structure by detecting the relationships of similarity and dissimilarity allowing us to select consistent groups of properties revealing implicit value/prices semantic chains [51,52].

Sub-Markets Analysis
Starting in the 1940s and 1950s, a group of US researchers who explored the functioning of local housing systems, began to develop "filtering models" as a conceptual framework to support applied studies [53,54]. A central assumption in the filtering models was the existence of real estate submarkets aimed at outlining the dynamics of house prices, quality changes and household choices.
However, the experimentation of filtering models did not produce a notion of univocal filtering in the housing literature [55].
In fact, in the literature, the concept of filtering is used within the urban economy to refer to many aspects, such as the life cycle processes of housing units (changes in their price, quality, income level of the occupant), and the life cycle processes of households (changes in the quality of their houses, due to variations in the real prices of the houses or in their real income levels).
Empirical analyses based on filtering have generally focused on a specific indicator of change, for example, the drop-in house prices [56], the turnover of houses detectable in the vacancy chains or the mobility of individual households affecting assets [57]. However, whatever the focal point, a rigorous analysis of the filtering necessarily implies a subdivision of the real estate market into several distinct segments among which existing households and houses move in interaction with new buildings. Urban analysts, while agreeing on the existence of market segments and their importance for the analysis of the real estate market [58][59][60], offer different points of view in identifying the empirical dimension underlying their identification. In general, the submarket, for the purposes of the analysis could be defined on the basis of the dwellings' location in the urban context (spatial submarkets) or on the basis of the real estate characteristics (structural submarkets), which would The varied combination of vulnerability and resilience factors affecting the several components of the human and urban capital reflected in these particular "real estate-scape" results in a variety of situations in which these values interact: Sometimes they compensate and somehow neutralize to each other; otherwise, they accumulate, affecting the expected price both upward and downward.
The approximation of this early analysis, as well as the wide dispersion of the scatter over the trend line and the low coefficient of determination, suggest carrying out a further study. The latter measure and maps the real estate-scape of the neighborhood in order to outline its structure by detecting the relationships of similarity and dissimilarity allowing us to select consistent groups of properties revealing implicit value/prices semantic chains [51,52].

Sub-Markets Analysis
Starting in the 1940s and 1950s, a group of US researchers who explored the functioning of local housing systems, began to develop "filtering models" as a conceptual framework to support applied studies [53,54]. A central assumption in the filtering models was the existence of real estate sub-markets aimed at outlining the dynamics of house prices, quality changes and household choices.
However, the experimentation of filtering models did not produce a notion of univocal filtering in the housing literature [55].
In fact, in the literature, the concept of filtering is used within the urban economy to refer to many aspects, such as the life cycle processes of housing units (changes in their price, quality, income level of the occupant), and the life cycle processes of households (changes in the quality of their houses, due to variations in the real prices of the houses or in their real income levels).
Empirical analyses based on filtering have generally focused on a specific indicator of change, for example, the drop-in house prices [56], the turnover of houses detectable in the vacancy chains or the mobility of individual households affecting assets [57]. However, whatever the focal point, a rigorous analysis of the filtering necessarily implies a subdivision of the real estate market into several distinct segments among which existing households and houses move in interaction with new buildings. Urban analysts, while agreeing on the existence of market segments and their importance for the analysis of the real estate market [58][59][60], offer different points of view in identifying the empirical dimension underlying their identification. In general, the submarket, for the purposes of the analysis could be defined on the basis of the dwellings' location in the urban context (spatial submarkets) or on the basis of the real estate characteristics (structural submarkets), which would identify housings with a similar quality compared to their position. In this regard, some researchers have defined the real estate sub-markets on the basis of spatial compartmentalization, i.e., by using a subdivision of the market into areas characterized by types of housing, socio-economic characteristics of households and environmental factors [61][62][63][64][65] or administrative boundaries [66][67][68][69] with references to population data; a priori knowledge of the market to create sub-markets [70]; identification of market areas and dwellings prices on the basis of perceptions of the sector professions [71,72]. Other researchers have suggested that secondary markets include all dwellings, regardless of their location, that have similar physical characteristics and represents relatively close substitutes for potential buyers [73,74].
William Grigsby was the first researcher who defined sub-markets in terms of "close substitutability" of dwellings [75]. According to this perspective, the real estate sub-market is made up of a number n of "neighboring substitutes" belonging to the same group, but "imperfect substitutes" of those belonging to other submarkets [76][77][78][79][80].
Some studies on secondary markets have explicitly recognized the common importance of spatial and structural characteristics in the definition of secondary markets, belong to this approach nested spatial/structural and demander-group-based submarkets.
In summary, there are four main filtering approaches in the literature for identifying submarkets: Spatial submarkets, structural submarkets, demander characteristics or considering the joint influence of structural and spatial factors.
Various models are proposed in the literature to identify and analyze submarkets: • Hedonic pricing models [81][82][83]

Identifying Real Estate Submarkets Based on Fuzzy K-Means Clustering
By cluster analysis, we mean a multivariate statistical technique, through which it is possible to obtain a groups structure from a certain population of data, that is, by grouping several similar units together in a certain number of groups.
The identified groups are characterized by being relatively homogeneous within them and heterogeneous among them. Homogeneity (heterogeneity) and heterogeneity (diversity) are assessed based on a defined set of variables. Grouping methods include traditional and fuzzy ones. In the first case, the objects belonging to a given group are selected by similarity (hard clustering), i.e., the "similar" objects are found in the same cluster. In the second case, the grouping of objects is carried out based on modulation of the degree of similarity (even partial) (soft clustering).
Fuzzy clustering makes use of fuzzy sets (defined by Zadeh) [99], which are sets whose elements have degrees of membership. More formally, supposed X is a set of data points. A fuzzy set A is formed if there exists a function f A : X → [0, 1] such that each element a ∈ A is of the form f A (x) = a, for some x ∈ X. That is, each data point in X is assigned a value between 0 and 1 which describes its degree of membership or the probability of its placement in the set A. In a fuzzy clustering, the data objects can belong to one or more clusters and their membership in a cluster corresponding to some probability.
The results of a fuzzy clustering can be represented by the k × n matrix U defined in Equation (3) [100]: where k is the resulting number of clusters and n is the number of data points in the original dataset? Each element in U is denoted by u ji where j ∈ {1, . . . , k} and i ∈ {1, . . . , n}.
In fuzzy clustering u ji may take a value between 0 and 1, i.e., u ji ∈ [0, 1]. U must satisfy two conditions in clustering k j=1 u ji = 1 (4) k j=1 u ji > 0 (5) Condition (4) requires that for each data object, the sum of its degrees of membership across all clusters be equal to 1. Condition (5), requires there to be no empty clusters.
One example of a fuzzy clustering algorithm is the fuzzy k − means algorithm (sometimes referred to as the c-means algorithm in the literature). It pursues the goal to minimize some objective function. Suppose we have a dataset D = {x 1 , . . . x n } and let q ∈ [0, 1]. Here, q is known as the fuzzifier, which determines the fuzziness of the resulting clusters. The larger the q value, the smaller the membership values u ji and, thus, the fuzzier the clustering. The objective function is defined as where d is an inner product metric function, and the V js are the centroids of the initial clustering of the data. This initial clustering of D is, of course, allowed to overlap if all points are included in at least one cluster. At any iteration, the degree of membership of the data point x i in the cluster j is defined by Equation (7): Each centroid V j is recalculated in the following way (7): After each iteration, the membership matrices of consecutive times steps are compared.
If max ji u k+1 ji − u k ji < ε, where 0 < ε < 1 is some predefined criterion for stability, then the fuzzy k-means algorithm is complete? Otherwise, the membership matrix, using new centroids, is calculated.
In order for d to be a distance measure and applied to a dataset {x 1 , . . . x n }, the following conditions must defined for indices 1 ≤ i, j, k ≤ n: There many kinds of distance measure. The most well-know and commonly used for numerical data is the Euclidean. The generalized Euclidean distance in p-dimensional between two points x i = x i1 , . . . , x ip and x j = x j1 , .., x jp is given by For numerical data other examples of distance function are the Manhattan distance (also known as taxicab distance), maximum distance, and average distance.

Results: Fragility and Resilience in Numbers and Comparisons
This section starts presenting the final part of the analyses, the one concerning the real estate survey and the interpretation of the findings. Then, these results will be presented in the context of the general assessment integrating all the analyses addressed to the social-urban-scape.

Real Estate-Scape. An Early Overview
The early surveys and the comparisons between the different urban areas showed the general wider range of the real estate market prices of the sample of Picanello, mostly due to the larger sample surveyed; nonetheless, in absolute terms, this range can be assumed as a measure of heterogeneity and complexity of this heritage (Figures 11 and 12). These characteristics affirm the wide quantitative and qualitative housings supply. The medium-low price level, approximately comparable to the new building cost, is a general index of vulnerability, but, at the same time, it outlines opportunities for future inclusive renovation programs, as indicated by the upper bound of the range.

Results: Fragility and Resilience in Numbers and Comparisons
This section starts presenting the final part of the analyses, the one concerning the real estate survey and the interpretation of the findings. Then, these results will be presented in the context of the general assessment integrating all the analyses addressed to the social-urban-scape.

Real Estate-Scape. An Early Overview
The early surveys and the comparisons between the different urban areas showed the general wider range of the real estate market prices of the sample of Picanello, mostly due to the larger sample surveyed; nonetheless, in absolute terms, this range can be assumed as a measure of heterogeneity and complexity of this heritage (Figures 11 and 12). These characteristics affirm the wide quantitative and qualitative housings supply. The medium-low price level, approximately comparable to the new building cost, is a general index of vulnerability, but, at the same time, it outlines opportunities for future inclusive renovation programs, as indicated by the upper bound of the range.

Results: Fragility and Resilience in Numbers and Comparisons
This section starts presenting the final part of the analyses, the one concerning the real estate survey and the interpretation of the findings. Then, these results will be presented in the context of the general assessment integrating all the analyses addressed to the social-urban-scape.

Real Estate-Scape. An Early Overview
The early surveys and the comparisons between the different urban areas showed the general wider range of the real estate market prices of the sample of Picanello, mostly due to the larger sample surveyed; nonetheless, in absolute terms, this range can be assumed as a measure of heterogeneity and complexity of this heritage (Figures 11 and 12). These characteristics affirm the wide quantitative and qualitative housings supply. The medium-low price level, approximately comparable to the new building cost, is a general index of vulnerability, but, at the same time, it outlines opportunities for future inclusive renovation programs, as indicated by the upper bound of the range.

Identifying Real Estate Submarkets in Picanello Based on a Fuzzy K-Medoids Clustering
As part of the analyses aimed at exploring the functioning of local housing systems, those based on filtering models presuppose the identification of real estate sub-markets.
Identifying a real estate submarket means finding properties that can be considered close substitutes for those belonging to the same group and imperfect for those belonging to different groups. An analysis aimed at identifying groups of properties within a sample as close substitutes for those belonging to the same group, can be carried out on the basis of two filtering models, the one based on the spatial characteristics and the one based on the real estate characteristics. In general, it is possible to achieve segmentation of a sample of properties by means of two approaches, the one supported by spatial submarkets analysis and by the one structural submarkets analysis. Certainly, in the case of the analysis of a sample of properties located in a well-defined area, such as that of a neighborhood, the real estate characteristics are the elements that offer better support for the segmentation of the sample.
However, a spatial segmentation of the sample can be carried out to provide a deepening of the submarkets identified based on the real estate characteristics [101][102][103]. Among the possible approaches proposed in the literature to identify and analyze submarkets, we have chosen fuzzy clustering. This approach allows you to partition a set of objects into two or more clusters, so that the objects within a cluster are similar and the objects in the different clusters are different, therefore, in general, it better meets the needs underlying the identification of submarkets proposed in the Grisby's approach. Among the centered-based algorithms proposed in the literature, we have chosen the k-medoids, which is a partitioning algorithm related to the k-means algorithm, which uses unlike the latter as centers the medoids instead of the average, i.e., a point in the dataset that is closer to the average. Therefore, the analysis aimed at identifying the submarkets of the neighborhood was conducted by means fuzzy clustering that generalizes partition clustering method k-medoids.
Fuzzy k-medoids clustering was implemented on a sample of 81 properties in the Picanello neighborhood. We analyzed three different datasets of the Picanello real estate market. The three datasets feature from a different configuration of the real estate characteristics.

1.
the first dataset is characterized on the basis of the six real estate characteristics: k e1 -location, urbanization and accessibility; k e2 -neighborhood characteristics: functional symbolic characteristics; k i -unit location within the building: panoramic quality and view, brightness, accessibility within the building; k t -technical characteristics: building overall technological quality, unit finishes and windows quality, maintenance levels; k a1 -building architectural quality; k a2 -unit architectural quality; 2.
the second dataset is characterized on the basis of four types of price: price/room, price/sm, price/room/k*, price/sm/ k*; 3.
the third dataset is characterized on the basis of six real estate characteristics (k e1 , k e2 , k i , k t , k a1 , k a2 ) and the four types of price (price/room, price/sm, price/room/k*, price/sm/ k*).
Where k * is a single score that aggregates the main real estate characteristics, expressing the overall quality associated with each jth property of sample X. The overall score k * is calculated by the following formula: where λ h is the weight of the hth characteristics, so that h λ h = 1; the scores of all features related to each k h are calculated similarly. The weights λ h are empirically defined to maximise the R 2 of the exponential simple regression function expressing the relationship between unit price (price/room or price/sm) and k * .
For the processing of the datasets on the real estate market of Picanello, we used the NCSS software, which supports a fuzzy k-medoids clustering.
In the NCSS software, the goodness of the fuzzy classification aimed at identifying the number of clusters that can be considered significant, is verified through three indices, namely, the value of the Average Silhouette, which provides information on the quality of the structure found (strong, reasonable, weak and none) cluster by cluster, and the normalized values of the partition coefficients of Dunn-Fc (U) and Kaufman-D (U).
The fuzzy k-medoids clustering on the first dataset of properties characterized on the basis of the six real estate characteristics (k e1 , k e2 , k i , k t , k a1 , k a2 ) produced four groupings, two, three, four and five clusters, which identifying fourteen potential real estate submarkets (Figures 13 and 14). In the NCSS software, the goodness of the fuzzy classification aimed at identifying the number of clusters that can be considered significant, is verified through three indices, namely, the value of the Average Silhouette, which provides information on the quality of the structure found (strong, reasonable, weak and none) cluster by cluster, and the normalized values of the partition coefficients of Dunn-Fc (U) and Kaufman-D (U).
The fuzzy k-medoids clustering on the first dataset of properties characterized on the basis of the six real estate characteristics , , , , 1 , 2 ) produced four groupings, two, three, four and five clusters, which identifying fourteen potential real estate submarkets (Figures 13 and 14).  The verification of the goodness of the classifications according to the three indices mentioned above, identified only in the first case a reasonable structure, while in all the other cases, weak structures were identified. The verification of the goodness of the classifications according to the three indices mentioned above, identified only in the first case a reasonable structure, while in all the other cases, weak structures were identified.
Based on that, only the sub-markets which have been identified by 1 and 2 in two-cluster fuzzy clustering can be considered significant for the segmentation of the real estate market of Picanello.
In particular, in the two-cluster classification, the properties of the dataset are distributed between 1 and 2 in the following way:  The verification of the goodness of the classifications according to the three indices mentioned above, identified only in the first case a reasonable structure, while in all the other cases, weak structures were identified.
Based on that, only the sub-markets which have been identified by Cluster1 and Cluster2 in two-cluster fuzzy clustering can be considered significant for the segmentation of the real estate market of Picanello.
In fact, the real estate characteristics of Centroid1 all have lower values, and those of Centroid2 all have higher values than the average values of the corresponding characteristics in the dataset.
The submarkets 1 is characterized not only by the lower values of the real estate characteristics, but also by a greater influence and of the same intensity as the k e1 , k e2 , k i , k a2 , by a lower influence from the k t and by an even less influence from the k a1 .
In reality, this result confirms the evidence in the literature on submarkets, which highlight a greater influence of k i [73], or k e1 , k e2 [72,74,104], or k i , k e1 , k e2 [69,105].
The submarkets 2 is characterized not only by the higher values of the real estate characteristics, but also by an influence of equal intensity of all k e1 , k e2 , k i , k t , k a1 , k a2 .
The spatial analysis of Cluster1 and Cluster2 highlights, besides the location of the properties in the Picanello neighborhood, also their membership function to the submarkets, which is represented in Figure 15 by the size of the spheres. The spatial analysis of 1 and 2 highlights, besides the location of the properties in the Picanello neighborhood, also their membership function to the submarkets, which is represented in Figure 15 by the size of the spheres. The properties belonging to submarket 1 are mostly distributed throughout the perimeter and in the inner area of the neighborhood. In general, it is noted that the properties belonging to the two This analysis highlights a concentration of the properties belonging to submarket 2 in the margin band of the neighborhood along via Duca degli Abruzzi to the east, via Messina to the south, behind at core of the ancient settlement of Ognina to the west and the presence of few properties in the inner area of the neighborhood.
The properties belonging to submarket 1 are mostly distributed throughout the perimeter and in the inner area of the neighborhood. In general, it is noted that the properties belonging to the two submarkets have homogeneous membership functions.
The fuzzy k-medoids clustring on the second dataset of properties characterized on the basis of the four types of price (price/room, price/sm, price/room/k*, price/sm/k*) produced four groupings, two, three, four and five clusters, which identify, also in this case, fourteen potential real estate sub-markets (Appendix B).
The verification of the goodness of the classifications according to the three indices mentioned above, identified only in the first case a reasonable structure, while in all the other cases weak structures were identified.
Based on that, only the sub-markets which have been identified by Cluster1 and Cluster2 in two-cluster fuzzy clustering can be considered significant for the segmentation of the real estate market of Picanello.
In fact, the real estate characteristics of Centroid1 all have lower values, and those of Centroid2 all have higher values than the average values of the corresponding characteristics in the dataset.
The submarkets 1 is characterized not only by the lower values for the four types of prices, but also by a greater and clearer influence of the price/room and price/room/ k*.
The spatial analysis also in this case highlights a concentration of the properties belonging to submarket 2 in the margin band of the neighborhood along the axis of via Duca degli Abruzzi to the east, via Messina to the south and west, Viale Ulisse and Viale Marco Polo to the north ( Figure 16).
In this case, properties belonging to sub-market 2 are also located along the median axis of the neighborhood in the north-east and south-west direction.
The properties belonging to the submarkets 1 are present throughout the perimeter of the neighborhood except for the north-west section but are also present in its central area.
In this case, the properties belonging to two submarkets have more heterogeneous membership functions.
The fuzzy k-medoids clustering on the third dataset of properties characterized on the basis of the four types of price (price/room, price/sm, price/room/k*, price/sm/ k*) and of the six real estate characteristics (k e1 , k e2 , k i , k t , k a1 , k a2 ) produced four groupings, two, three, four and five clusters, which identifying fourteen potential real estate sub-markets.
In this case, the verification of the goodness of the classifications identified in all cases, weak structures.
The results of the analysis do not allow identification of sub-markets which can be significant for the dataset.
Even if the structures found are weak, we can still compare some results with those found in the two previous analyses: • The influence of the six real estate characteristics is not reconfirmed, result that it was highlighted in the analysis of the first data set; • A net influence is confirmed in the classification of the two real estate price/room and price/room/k * , which reconfirms a data highlighted in the analysis of the second dataset. The centroid of the first cluster is property 25 and that of the second cluster is property 26. The submarket identified by 1, i.e., sub-market 1, contains the worst properties in terms of the four types of price, the second submarket identified by 2, i.e., sub-market 2, contains the best ones.
In fact, the real estate characteristics of 1 all have lower values, and those of 2 all have higher values than the average values of the corresponding characteristics in the dataset.
The submarkets 1 is characterized not only by the lower values for the four types of prices, but also by a greater and clearer influence of the / and / / k*. The spatial analysis also in this case highlights a concentration of the properties belonging to submarket 2 in the margin band of the neighborhood along the axis of via Duca degli Abruzzi to the east, via Messina to the south and west, Viale Ulisse and Viale Marco Polo to the north ( Figure 16). In this case, properties belonging to sub-market 2 are also located along the median axis of the neighborhood in the north-east and south-west direction.
The properties belonging to the submarkets 1 are present throughout the perimeter of the neighborhood except for the north-west section but are also present in its central area.
In this case, the properties belonging to two submarkets have more heterogeneous membership functions.
The fuzzy k-medoids clustering on the third dataset of properties characterized on the basis of the four types of price( / , / , / /k*, / / k*) and of the six real estate characteristics ( 1 , 2 , , , 1 , 2 ) produced four groupings, two, three, four and five clusters, which identifying fourteen potential real estate sub-markets. In this case, the verification of the goodness of the classifications identified in all cases, weak structures.
The results of the analysis do not allow identification of sub-markets which can be significant for the dataset.

Overall Results
The quantitative results of the housing market survey, and namely, the cluster analysis results, have been integrated within the general assessment model thus providing a complete, although not exhaustive, an overview of the issues that are usually assumed as the main drivers of urban fragility and resilience. Figure 17 provides a synopsis of the fragility-resilience indices of Picanello (ACE 12) compared to the other ACEs and Catania. The upper table provides a simplified dendrogram of the WBS within which the different indices have been framed, and the aggregated scores for the different ACEs, the radar graph below allows us to identify and measure weaknesses and strengths in terms of social-urban fragility. (See Table 3).

Discussion
The assessments carried out so far reveal different aspects of the fragility of Picanello concerning the different perspectives of human and urban capital. The former results significantly affected by (absolute, not relative) criticalities in the fields of education, lifestyle, labor market prospects. The latter presents specific urban-environmental (air quality, waste recycling) [107] and urban planning (public facilities and utilities) criticalities, aspects that Picanello shares with other urban areas. Nonetheless, if combined with the aspects of social fragility, the lack of the public sector can hinder the prospect of development and improvement of global standards of livability, participation and inclusion.
Aspects of resilience are found: As regards human capital, concerning education (which is expected to be higher in a neighborhood located in a strategic area, and including a valuable building heritage) and employment; as regard for urban capital, resilience is in the building heritage, symmetrically to the fragility of the urban-environmental heritage.
According to the synecdoche of fragility, also the real estate-scape adds further ambiguities to those related to the human-urban-scape. The synthetic indices reveal a sufficient quality level of the housings supply, but lower unit prices indices.
Another important index of the real estate capital asset, especially for the expectations of the development of a central area supported by concrete improvements in urban social capital, is the capitalization rate [108,109]. Its relative level is almost sufficient, which indicates a generalized propensity to deferral in the real estate investment field. This degree of confidence, still potential, can grow if the environmental-urban criticalities are reduced by means of constructive urban policies.
Final remarks concern the map of the housing, monetary and not monetary, values, as outlined by the fuzzy-medoid cluster analysis. A structure index was sought in the surveys carried out, which  Sub-market Structure   01  02  03  04  05  06  07  08  09  10   11  12  13  14  15  16  17  18 19 Catania Figure 17. The overall comparative assessment of the different ACEs at the level of the aggregated fragility/resilience factors. The neighborhood of Picanello is in red, and Catania is in light blue.

Discussion
The assessments carried out so far reveal different aspects of the fragility of Picanello concerning the different perspectives of human and urban capital. The former results significantly affected by (absolute, not relative) criticalities in the fields of education, lifestyle, labor market prospects. The latter presents specific urban-environmental (air quality, waste recycling) [106] and urban planning (public facilities and utilities) criticalities, aspects that Picanello shares with other urban areas. Nonetheless, if combined with the aspects of social fragility, the lack of the public sector can hinder the prospect of development and improvement of global standards of livability, participation and inclusion.
Aspects of resilience are found: As regards human capital, concerning education (which is expected to be higher in a neighborhood located in a strategic area, and including a valuable building heritage) and employment; as regard for urban capital, resilience is in the building heritage, symmetrically to the fragility of the urban-environmental heritage.
According to the synecdoche of fragility, also the real estate-scape adds further ambiguities to those related to the human-urban-scape. The synthetic indices reveal a sufficient quality level of the housings supply, but lower unit prices indices.
Another important index of the real estate capital asset, especially for the expectations of the development of a central area supported by concrete improvements in urban social capital, is the capitalization rate [107,108]. Its relative level is almost sufficient, which indicates a generalized propensity to deferral in the real estate investment field. This degree of confidence, still potential, can grow if the environmental-urban criticalities are reduced by means of constructive urban policies.
Final remarks concern the map of the housing, monetary and not monetary, values, as outlined by the fuzzy-medoid cluster analysis. A structure index was sought in the surveys carried out, which is slightly lower than the average, due to the strong heterogeneity of the building heritage of the area. Therefore, only a division into two clusters reaches a goodness equal to 1. This result can be interpreted in the light of the previous remarks concerning the reduced perception of a clearer spatial structure in which the preference system recognizes contexts with a higher urban identity, currently reduced in some areas by spread replacements of the original building stock.
Some limitations of the research concern the datasets resulting too aggregate in respect of such a heterogeneous neighborhood so that some specific characteristics have to be highlighted by means of the cluster analysis at the abstract level of the real estate housing market prices.

Conclusions
The global cognitive and operational context of project and urban planning integrates and coordinates multiple languages-each of which having its own rules and ambiguities. This assessment experiment is inspired by the idea of a structure of value and of a grammar of valuations, aimed at systematizing in a unitary pattern a set of findings having as "value attributes" the degree of fragility/resilience and as "value bearers" the urban and the human capital.
Social and territorial sciences commit to creating urban vulnerability and fragility maps for which statistics survey make available a complex fabric of indices. The Science of valuation contributes targeting this information support in the light of the concept of capital assumed in its broader and constructive meaning, of value stock accumulated in the enduring buildings and layered in the depth of the personal and social subjectivity [109][110][111][112][113].
Even if represented in numbers, indices and market prices, Picanello appears to have a social system at the same time unitary and internally contradictory, a microcosm of a metropolis, still pervaded by the feeling of inclusion, and animated by the mixture of diverse folks, whose imprinting research is inspired by the real estate-scape can better highlight.
In this specific field of research, real estate manifests the complex relationships between values (what is important and what do we actually mean with this importance) and prices (the economic-monetary abstraction and generalization of this importance).
With reference to the case of Picanello in Catania, the analysis carried out so far, identified some factors influencing the consistency and/or decaying of social capital; then they have been connected to the local housing market in as much as they are metabolized by the "economic communication" developing according to this particular economic, financial and monetary logic.
The findings confirm that a more marked presence of the public action and intentionality could trigger the virtuous circle of the recovery of a central area characterized by the contiguity to the valuable waterfront urban neighborhoods which Picanello cannot still benefit from.
The limitations concerning the difficult overlapping of the value-maps (as for social, economic and real estate issues) must be overcome. Then, the possibilities for further studies of this experiment will involve the extension of such a qualitative, quantitative and monetary description over the whole urban context in order to more strongly outlying the urban, human and real estate-scape of the city of Catania.