## 1. Introduction

An urban system is a complex entity, composed of various elements with specific physical, morphological, environmental, and socio-economic characteristics. Often, in order to analyze an area of study related to urban analysis problems, it is useful to partition it into a set of homogeneous areas with respect to specific characteristics. In literature, there are various studies in which unsupervised methods are proposed to segment the area of study into homogeneous zones in order to analyze specific problems. Various authors propose automatic classification methods to partition urban areas and elements using raster remote sensing data. In Reference [

1] a genetic algorithm is applied in order to automatically extract the classification rules of urban areas from remote sensing data. In Reference [

2], a framework based on expert knowledge is applied in order to segment coastal areas using raster remote sensing data. In Reference [

3], a new method based on unsupervised change detection focused on individual buildings is applied to very high-resolution remote sensing imagers to extract elements in urban systems. In Reference [

4], a hierarchical object-oriented model is proposed to classify objects in an urban area from high-resolution satellite images. In Reference [

5], a multiple-kernel learning model is proposed to classify urban areas from spectral and LiDAR raster data. A review of classification methods proposed to classify urban land cover through the use of raster LiDAR remote sensing images is presented in Reference [

6].

Other recent studies propose decision-making spatial analysis models in which GIS and fuzzy systems are applied in engineering optimization analysis to solve decision-making problems, such as selection of the best logistic locations [

7], the study of the prevention of a stroke [

8], the optimization of green routes for city logistics centers [

9], and the selection of the most suitable sites for wind-farm installments [

10].

Recently, thanks to the availability of various thematic data at different scales from different institutional sources, together with the use of socio-demographic census data, it has been possible to implement methods for the unsupervised classification of urban systems that take into consideration knowledge of the urban system and expert knowledge of the problem being analyzed. In Reference [

11], the area of study is partitioned into homogeneous zones based on morphological and soil characteristics in order to analyze the vulnerability of the aquifer to pollution; a fuzzy algebraic structure is applied to assess the aquifer vulnerability in any zone. In Reference [

12], a multiple-level association rule mining method is applied to spatiotemporal socio-economic and land cover datasets based on a hierarchical classification scheme to extract relations between objects in the area of study and classify them.

In Reference [

13], a simulated annealing method is applied to partition an area of study into homogeneous zones based on socio-economic characteristics. In Reference [

14], a partition of the urban system in census zones is performed in order to study the spatial distribution of socio-economic characteristics. In Reference [

15], a multi-objective approach is applied in order to partition the municipalities of the region of Parana in Brazil into microregions; this approach maximizes population homogeneity and the medical procedure used in any microregion and minimizes inter-microregion traveling.

In this study, we propose a novel model based on a Mamdani fuzzy rule-based system [

16,

17] aimed at partitioning an urban system into homogeneous zones, called urban contexts; each urban context is labeled with a specific urban class based on a specific taxonomy related to the problem being studied. Our goal is to model the knowledge and approximate reasoning of domain experts in order to apply them to partition the urban system.

Fuzzy logic plays a key role in approximate reasoning, and Fuzzy Logic Systems [

18,

19,

20] are implemented to manage approximate knowledge in order to solve specific problems through the use of approximate reasoning. The Mamdani fuzzy rule-based model is the most well-known fuzzy logic system model; it has been successfully applied in many fields, such as automatic control [

21], expert systems [

22], mobile robots [

23], and computer vision [

24].

In References [

25,

26], approaches based on the Mamdani fuzzy rule-based system model for unsupervised classification are proposed. Our objective is to use a Mamdani fuzzy rule-based system to manage the experts’ approximate reasoning applied to classify urban contexts.

Our approach is independent of the problem analyzed; initially, we partition the area of study into homogeneous zones provided by census atomic elements called microzones. We follow Italian Presidential Decree no. 138 of 1998, Article 1 (

http://def.finanze.it/DocTribFrontend/getAttoNormativoDetail.do?ACTION=getSommario&id={CE130656-7850-4531-9B95-F17CC19790C4}) of which defines a microzone as a homogeneous portion of the urban system, which may include one municipality, a portion thereof, or groups of municipalities, characterized by similar environmental and socio-economic characteristics. The microzone represents a portion of the municipality or, in the case of areas consisting of groups of municipalities, an entire municipal territory homogeneous in terms of its urban, historical-environmental, and socio-economic characteristics, as well as in the provision of urban services and infrastructure. For example, in each microzone, buildings are predominantly uniform in terms of their construction features, construction period, and residential/industrial/commercial use.

The first step of our method concerns the acquisition of different, not normalized thematic data from various institutional sources, including from the last microzone census database.

Subsequently, a homogeneous knowledge base of the urban system analyzed is created, in order to extract a set of synthetic indicators representing the characteristics of the urban system related to the problem analyzed. These indicators express the input variables of a fuzzy rule set extracted by domain experts, in which the output variable expresses an urban class.

A Mamdani fuzzy rule system is applied to classify the microzones, assigning them a specific class; finally, a dissolve spatial operator is used to aggregate microzones that are spatially contiguous classified in the same urban class in urban contexts; in addition, we assess the membership degree of each urban context to its class, by using a weighted average of the membership degrees to this category calculated in any microzone included in the urban context. This membership degree represents the uncertainty of the attribution of the urban context to its urban class and provides an evaluation of the reliability of the classification.

The main advantages of the proposed model are its independence from the problem analyzed and its usability. In fact, our framework can be applied to any type of problem concerning the analysis of urban systems and streamlines and make the construction of knowledge transferred by domain experts more efficient. Finally, the assessment of the membership degree of the urban contexts to their urban classes allows the analyst to evaluate the reliability of the resultant partition.

In the next section, the proposed model is described in detail; in order to show the ways in which the components of our model are applied, a case study concerned with partitioning an urban system in the contexts in which urban classes are typified according to different residential densities is explored.

In

Section 3, the area of study and the institutional datasets used in our experiments are described;

Section 4 presents the results of our experiments; and some final considerations are reported in

Section 5.

## 2. The Proposed Model

Our model is composed of a set of five phases, as shown in

Figure 1.

Phases 1a and 1b are executable in parallel.

Phase 1a (Data acquisition) concerns the acquisition of the datasets from institutional sources. A set of staging procedures are required to allow for the reconciliation of these inhomogeneous data (for example, to carry out the transformation and conversions of spatial data in a unique coordinate system and to correct spatial topological errors) and the creations of relations between the various datasets. The output of this phase is given by the homogeneous spatial database of the area of study.

In phase 1b (Indicators and fuzzy rule set creation) the various physical, environmental, and socio-economic indicators are defined and the fuzzy rule set is created; this phase is executed with the contribution of domain experts. To model the expert knowledge and construct the fuzzy rules, we created a fuzzy partition of the domain of each indicator in which any fuzzy set is assigned by using a triangular or semi-trapezoidal fuzzy number and is titled with a linguistic label assigned by the domain expert.

In phase 2 (Calculus of the microzone indicators), the spatial analysis processes need to calculate the indicators are implemented. Each indicator represents a summary of the specific characteristics of the microzone; it is calculated by applying the formulas created in phase 1b and by using a set of geoprocessing and statistical operators applied to entities and characteristics in the spatial database.

In phase 3 (Fuzzy rule system execution) for each microzone the Mamdani fuzzy rule system is executed in order to assign the microzone to a specific urban class. The indicators are fuzzified using a fuzzification component; then, the fuzzy inference component is applied by using the Mamdani min and max operators; and the urban class assigned to the microzone is given by the consequent of the fuzzy rule with the greatest strength.

In phase 4 (Homogeneous urban contexts creation), the adjoining microzones belonging to the same urban class are dissolved and the thematic map of the urban contexts of the area of study is created.

#### 2.1. Phase 1a—Data Acquisition

In this phase, data concerning the area of study are acquired from various institutional sources. The output of this phase is a spatial database implementing the homogenous knowledge base of the area of study. A spatial dataset is provided by the microzone census data, including the polygon spatial data corresponding to the microzones. Other datasets are needed to extract the synthetic indicators related to different information layers, such as population, buildings, roads, urban green, schools, and infrastructures.

A set of geoprocessing activities are required in order to normalize the spatial datasets; all the datasets must be converted using a unique coordinate system and a topological check is necessary to verify the integrity of the dataset. Other geoprocessing activities could be carried out to extract and normalize the thematic data, such as:

- -
Extracting themes from a dataset in various formats;

- -
Merging datasets corresponding to a theme and distributed per tiles, clipped onto the area of study;

- -
Applying spatial operators related to any feature of the theme information, inserted as annotation texts (for example, the road name assigned to any polyline of a road network).

A data cleaning activity on the data fields it required in order to verify their integrity and accuracy, to delete outliers, and to correct inconsistent data and redundancies.

Finally, all the themes and tables are imported in a spatial database and the relation between them is established.

#### 2.2. Phase 1b—Indicators and Fuzzy Rule Set Creation

The indicators needed to classify the microzones are evaluated by domain experts. In our experiment, the experts consider 14 indicators related to various thematic layers that characterize the areas of study and which are needed to evaluate to which urban class the microzone belongs. In

Table 1, all the indicators are described; each indicator is assigned an identify and the type of indicator is reported, i.e., the thematic layer to which it refers, a brief description, and the unit of measurement.

After defining the indicators, the domain experts create a fuzzy partition of each indicator by using triangular and semi-trapezoidal fuzzy numbers to create the fuzzy sets. The fuzzy partitions of the indicators in

Table 1 are shown in

Table 2, in which the identifier of the indicator, a label assigned to the fuzzy sets, the inf, mean and sup values of the fuzzy number and the type of fuzzy set (ST = Semi-Trapezoidal, TR = Triangular) are reported.

In order to extract the fuzzy rules, the experts define the taxonomy of the urban area classes. In our experiment, the following set of urban area classes is considered, in which each class characterizes a type of residential or rural zone of the urban system.

Each class in

Table 3 corresponds to a fuzzy set of output linguistic variable Z defined in the domain [0,1] and, following an increasing order from 0 to 1, represents the impact of residential settlements on the area. The first fuzzy set is a semi-trapezoidal fuzzy set representing a predominantly rural or wooded area; the last fuzzy set is a semi-trapezoidal fuzzy set representing a compact residential old town. The intermediate fuzzy sets are triangular. These fuzzy sets are defined in

Table 4 and are graphically presented in

Figure 2.

Based on their knowledge, the experts extract the set of fuzzy rules needed to evaluate the urban class to which each microzone belongs. In our experiment, the 14 indicators are used as input variables in the antecedent of each rule and output variable Z is used in the consequent, labeled as presented in

Table 3. The fuzzy rule set is composed of fuzzy rules extracted by the experts, written in the following form:

where I

_{1}, I

_{2}, I

_{n}, are the input variables given by the linguistic labels of the fuzzy sets of the indicators and Z is the output variable. The operator Δ

_{i} (i = 1, …, n) is given by an AND or an OR connective. We construct the fuzzy rule set considering only AND connectives, splitting rules in which there are OR connectives in the antecedent. To show the splitting process of the rules, we take into consideration the following subset of fuzzy rules created by the experts:

**IF** (I_{4} == Null) AND (I_{6} == Discrete OR I_{6} == High) AND (I_{7} == High) **THEN** Z == Residential old town

**IF** (I_{1} == Discrete OR I_{1} == High) AND (I_{3} == Discrete OR I_{3} == High) AND (I_{8} == Null) AND (I_{12} == High) **THEN** Z == Comfortable residential zone

**IF** (I_{2} == Null) AND (I_{7} == Scanty OR I_{7} == Mean) AND (I_{12} == High) AND (I_{14} == Discrete OR I_{14} == High) **THEN** Z == Comfortable residential zone

**IF** (I_{2} == Discrete OR I_{2} == High) AND (I_{6} == Null) AND (I_{7} == Scanty) **THEN** Z == Industrial zone

After the rule-splitting process, we obtain the following final fuzzy rules:

**R**_{1}: **IF** (I_{4} == Null) AND (I_{6} == Discrete OR I_{6} == High) AND (I_{7} == High) **THEN** Z == Residential old town

**R**_{2}: **IF** (I_{4} == Null) AND (I_{6} == High) AND (I_{7} == High) **THEN** Z == Residential old town

**R**_{3}: **IF** (I_{1} == Discrete) AND (I_{3} == Discrete) AND (I_{8} == Null) AND (I_{12} == High) **THEN** Z == Comfortable residential zone

**R**_{4}: **IF** (I_{1} == High) AND (I_{3} == Discrete) AND (I_{8} == Null) AND (I_{12} == High) **THEN** Z == Comfortable residential zone

**R**_{5}: **IF** (I_{1} == Discrete) AND (I_{3} == High) AND (I_{8} == Null) AND (I_{12} == High) **THEN** Z == Comfortable residential zone

**R**_{6}: **IF** (I_{1} == High) AND (I_{3} == High) AND (I_{8} == Null) AND (I_{12} == High) **THEN** Z == Comfortable residential zone

**R**_{7}: **IF** (I_{2} == Null) AND (I_{7} == Scanty) AND (I_{12} == High) AND (I_{14} == Discrete) **THEN** Z == Comfortable residential zone

**R**_{8}: **IF** (I_{2} == Null) AND (I_{7} == Mean) AND (I_{12} == High) AND (I_{14} == Discrete) **THEN** Z == Comfortable residential zone

**R**_{9}: **IF** (I_{2} == Null) AND (I_{7} == Scanty) AND (I_{12} == High) AND (I_{14} == High) **THEN** Z == Comfortable residential zone

**R**_{10}: **IF** (I_{2} == Null) AND (I_{7} == Mean) AND (I_{12} == High) AND (I_{14} == High) **THEN** Z == Comfortable residential zone

**R**_{11}: **IF** (I_{2} == Discrete) AND (I_{6} == Null) AND (I_{7} == Scanty) **THEN** Z == Industrial zone

**R**_{12}: **IF** (I_{2} == High) AND (I_{6} == Null) AND (I_{7} == Scanty) **THEN** Z == Industrial zone

#### 2.3. Phase 2—Calculus of the Microzone Indicators

To calculate the indicators in each microzone, specific spatial analysis functions are applied. For example, the indicator I

_{1} in

Table 1 is calculated by selecting the residential buildings in the area of study and extracting the total surface area covered by residential buildings and the number of residents per microzone. Finally, for each microzone, the ratio between this total surface area and the number of residents is calculated.

A hierarchy of spatial analysis processes could be needed in order to calculate the value of an indicator. In our experiment, to calculate the indicators I

_{11}, I

_{12}, I

_{13} and I

_{14}, is necessary to calculate further parameters, labeled as II level indicators, described in

Table 5.

The indicator I_{11} is obtained as a weighted mean of the indicators I_{11a}, I_{11b} and I_{11b}, where the weights are, respectively, residents aged between 5 and 9 years, residents aged between 10 and 14 years, and residents aged between 15 and 19 years.

Formally, let n_{5–9} be the number of residents in the microzone with an age in the range of 5–9 years, let n_{10–14} be the number of residents in the microzone with an age in the range of 10–14 years, and let n_{15–19} be the number of residents in the microzone with an age in the range of 15–19 years.

The indicator I

_{11} is given by the formula:

The indicator I

_{12} is obtained as a weighted mean of the indicators I

_{12a} and I

_{12b}.

where w

_{12a} and w

_{12b} are the weights assigned, respectively, to the indicators I

_{11a} and I

_{11b.} The experts set w

_{12a} = 3 and w

_{12b} = 7, considering the influence of railway/subway station services to be greater than that of bus services.

The indicator I

_{13} is calculated as:

The indicator I

_{14} is calculated as:

#### 2.4. Phase 3—Fuzzy Rule System Execution

In this phase, a Mamdani fuzzy rule-based system is used to classify the microzones.

In

Figure 3, the fuzzy rule-based system used is schematized.

From the spatial database constructed in the previous phase, the microzone dataset containing the crisp values of the indicators calculated for each microzone is extracted. The Fuzzifier component imports these indicator values and assigns each indicator the membership degree to its fuzzy sets. Then, the Fuzzy Inference Engine component reads the membership degree of the fuzzy sets related to each indicator and performs the inference process by calculating the strength of each fuzzy rule in the fuzzy rule set.

The min operator is applied to the AND connectives in the antecedent of the fuzzy rule to calculate its strength. The Fuzzy Inference Engine carries out the aggregation process to construct the output final fuzzy set. Aggregation is the process by which the truncated output fuzzy sets in each rule are combined into a single fuzzy set that represents the output aggregated fuzzy set.

In order to show the aggregation process, we consider a system formed of two fuzzy rules in the form:

where A

_{1} and A

_{2} are two fuzzy sets of the linguistic input variable I

_{1}, B

_{1} and B

_{2} are two fuzzy sets of the input linguistic variable I

_{2}, and C

_{1} and C

_{2} are two fuzzy sets of the output variable Z.

Now let us suppose that, after the fuzzification process, we obtain the following membership degree for the input variables: A_{1} = 0.3, B_{1} = 0.5, A_{2} = 0.7, B_{1} = 0.8.

The strengths of the two rules are given by:

In the aggregation process, we construct the output fuzzy set given by:

In

Figure 4, the output fuzzy set constructed in this example is presented.

The defuzzification process of the output fuzzy set is carried out using the discrete Center of Gravity (CoG) method, with the following formula:

where the two integrals are extended in the range [0,1], which is the domain of the output variable Z.

We classify the microzone by assigning it to urban class label of the output variable fuzzy set with a greater membership degree in the point $\widehat{\mathrm{Z}}$; the degree of membership of the microzone to this class is given by the degree of membership of the output variable to C in the point $\widehat{\mathrm{Z}}$.

In

Figure 5, the results of the defuzzification process are shown. As

${\mathrm{C}}_{1}\left(\widehat{\mathrm{Z}}\right)$ is greater than

${\mathrm{C}}_{2}\left(\widehat{\mathrm{Z}}\right)$, we assign the microzone to class C

_{1} with a membership degree given by

$\mathrm{C}\left(\widehat{\mathrm{Z}}\right)$.

The Center of Gravity

$\widehat{\mathrm{Z}}$ can be easily calculated considering N discrete points of C(Z) and discretizing the formula (7), obtaining:

In

Figure 5, we consider six points corresponding to the boundaries of the segments of the broken line Z, obtaining using the formula (9)

$\widehat{\mathrm{Z}}$ = 0.52.

#### 2.5. Phase 4—Homogeneous Urban Context Creation

In this phase, the area of study is partitioned into urban contexts. Each urban context is obtained by dissolving adjoining microzones belonging to the same urban class; then, the thematic map of the urban contexts of the area of study is created.

A weighted mean of the membership degree of the microzones forming an urban context is calculated, to extract the reliability of the urban context; the weight is given by the area of the microzone as the greater the surface of a microzone included in a context, the greater its impact on the reliability of the classification of the context.

## 4. Test Results

We tested our framework on a Pentium I7 dual core platform using the tool GIS ESRI ArcGIS 10.5; all the spatial analysis processes were implemented as functions in the tool GIS; and the fuzzy inference system was implemented in C++ language and incapsulated in the tool GIS.

In order to calculate the indicators needed to test our model, a set of spatial operators, such as spatial intersects and spatial joins, was used to calculate the indicators assigned to the microzones starting from the data acquired from the various spatial datasets. Then, the processes applied to extract the indicators were synthetized.

To calculate the indicators I_{1} and I_{2}, the polygonal building dataset was partitioned into residential and industrial buildings in order to extract, respectively, the area covered by residential and industrial buildings per microzone.

Indicator I_{3}, given by the mean square meters of green areas per resident, was calculated by selecting the urban green areas and calculating the sum of urban green areas covering any microzone. Finally, this area was divided by the number of residents in the microzone.

Indicator I_{4} was calculated by dividing the sum of green areas in the microzone by the area of the microzone.

To calculate the indicators I_{5}, the district urban roads were selected from the road network layer and the sum of the lengths of the selected arcs falling in each microzone was calculated; finally, this value was divided by the sum of the length of all the road arcs falling in the microzone. Indicator I_{6} was calculated by selecting the district urban roads with a width of less than 7 m and dividing the sum of the selected arcs fallings in any microzone by the sum of the district urban road arcs falling in the microzone.

Indicator I_{7} was calculated by dividing the number of residents in any microzone by the area of the microzone in square kilometers.

To calculate the indicators I_{8}, I_{9}, and I_{10}, the building and dwelling census dataset was used, extracting, for each microzone, respectively, the number of residential buildings built before 1945, the number of dwellings with at least one resident, and the number of residential buildings with at least 16 dwellings, and dividing them, respectively, by the number of residential buildings, the number of dwellings, and the number of residential buildings in the microzone.

The II level indicators I_{11a}, I_{11b} and I_{11c} were calculated by extracting from the point school layer, respectively, the primary, low secondary, and secondary schools, and constructing circular buffer areas with a radius of 500 m centered in any school. Then, for any type of school, the area of the microzone covered by the calculated buffer areas was extracted and divided by the area of the microzone.

The II level indicators I_{12a} and I_{12b} were calculated by extracting from the point transport facility layers, respectively, the bus stops and the railway stops, and constructing circular buffer areas with a radius of 100 and 300, respectively, centered in any stop. Then, for any type of stop, the area of the microzone covered by the buffer areas calculated was extracted and divided by the area of the microzone.

The II level indicators I_{13a} and I_{13b} were calculated by selecting, respectively, microzones including coastal areas and those containing a maritime terminal.

The II level indicators I_{14a} and I_{14b} were calculated by extracting, respectively, the polygon hospital and sports facility layers and selecting the microzones including the selected elements.

For brevity, we showed the thematic maps obtained for the indicators I

_{2} (

Figure 7) and I

_{4} (

Figure 8) in which an equal interval classification method of the indicator is applied.

After calculating the crisp values of the indicators, we applied the fuzzification process, executing the fuzzifier component of the fuzzy rule system.

Figure 9 and

Figure 10 present two thematic maps of, respectively, the indicators I

_{2} and I

_{4}, in which each microzone is assigned the label of the fuzzy set to which the microzone belongs with the highest membership degree.

The two maps in

Figure 9 and

Figure 10 were obtained after the fuzzification process and highlight the microzones characterized by the indicator. In

Figure 9, the microzones classified as

High (in red) are characterized by a strong presence of industrial areas. In

Figure 10, the microzones classified as

High (in dark green) are largely covered by urban or overgrown green.

After the fuzzification process, the fuzzy inference engine component was initiated; a set of about 100 fuzzy rules created by the domain experts was used. Finally, the defuzzification process was executed and the appropriated urban area class was assigned to each microzone.

The thematic map in

Figure 11 show the classification results. In this map, the urban area classification of the microzone is shown.

In order to evaluate the performance of the classification, we compared the results with the supervised urban area classification of the microzones performed by the experts. For each class, we calculated the accuracy, precision, and recall (or sensitivity) indexes. This calculus was performed by extracting, from the confusion matrix, the TP, TN, FP, and FN parameters, where:

- -
TP (True Positive) is the number of microzones correctly assigned to the class;

- -
TN (True Negative) is the number of microzones correctly not assigned to the class;

- -
FP (False Positive) is the number of microzones wrongly assigned to the class;

- -
FN (False Negative) is the number of microzones wrongly not assigned to the class.

The three indexes are given by:

Table 7 show the classification results; the three indexes were calculated for any class.

These results show that the classification of the microzones obtained by applying our model is almost similar to the supervised one attributed by the experts. The only deviations are present for the indexes Accuracy and Recall in the classes Fragmented rural/wooded zone and Sprawl; two of the 18 microzones classified by the experts as Fragmented rural/wooded zone by using our model are classified as Sprawl.

Finally, adjoining microzones belonging to the same class were dissolved, forming urban contexts.

The Municipality of Pozzuoli is partitioned into 60 urban contexts, as shown in the map in

Figure 12.

The only urban context classified as Residential old town (in magenta) is an area that includes the historical center of Pozzuoli. The urban contexts classified as Coastal residential zone (in light blue) are residential coastal areas. The other coastal areas are, respectively, the maritime industrial area, classified as Industrial zone, and an area given by a maritime non-residential microzone, classified as Fragmented rural/wooded zone since it is not a residential zone and a high percentage of the zone is covered by vegetation. All the contexts classified as Industrial zone (in red) are areas where most of the buildings are industrial buildings or warehouses. The contexts classified as Downtrodden residential zone (in orange) are residential areas with a high density of residential housings and with a high population density. The other average residential contexts are classified as Comfortable residential zone (in light green); in these zones, the population density and the number of dwellings per residential building are not high; in addition, these zones are mostly covered by transportation services and schools and contain public green areas. The contexts classified as Sprawl (in brown) are areas where the density of residential buildings is sparse; they are probably urban agglomerations in recent, slow, and unplanned expansion. Finally, the contexts classified as Fragmented rural/wooded zone (in green) are areas predominantly or completely covered with vegetation.

In

Figure 13, a thematic map with the reliability of the results is presented. The reliability is calculated as a weighted average of the membership degree to the urban area class of the microzones included in the context where the weight is given by the area of the microzone.

There are four contexts with a low reliability, in the range of 0.2–0.4: three of these contexts are classified as Sprawl and the last as Downtrodden residential zone. In all these contexts, microzones with a not high degree of membership to their urban area class, meanly under the value of 0.4, are included.

These results suggest the need for a finer classification of urban areas in order to improve the reliability of urban contexts with a low reliability. In fact, in microzones classified as a specified urban area with a low membership degree, there are probably different types of urban areas; a finer classification could also take into account classes of urban areas to which microzones belong with a slightly lower degree of membership. For example, the context with low reliability classified as Downtrodden residential zone is given by a microzone classified as Downtrodden residential zone with a membership degree of 0.36 and belonging to the class Industrial zone with a membership degree of 0.31; this microzone included a densely populated residential area and a non-residential area with industrial premises; a finer classification of this microzone could consider both these classes in order to characterize the type of urban area that it represents in greater detail.