**2. Study area and preparation of the conditioning factors**

This study focuses on Libya, a country in the Maghreb region of North Africa (**Figure 1**). Libya borders the Mediterranean Sea to the north and Egypt to the east. Along the southeast of Libya is Sudan, Chad. To the south is Niger. Algeria and Tunisia constitute the western border. Libya is the 17th largest nation in the world with a landmass of over 1,759,540 km2 . The study area in the northern part of Libya covers six districts, namely, Darnah, Al Jabal Al Akhdar, Benghazi, Al Marj, Al Qubbah, and

**Figure 1.** *(a) Map of Libya with northern part highlighted, (b) the location of the urban area, (c) the road networks in the study area, and (d) mosaicked Landsat images.*

highest cloud cover was 1.03%, which does not pose a problem for land use information extraction from the study area. Since the images have overlapping areas, they were preprocessed and mosaicked to create one seamless image of the area for

**Image ID Acquisition date Raw Path Cloud cover (%)** Landsat 8 OLI 1 1 March 2017 38 182 0.77 Landsat 8 OLI 2 13 February 2017 39 182 1.03 Landsat 8 OLI 3 4 February 2017 38 183 0.00 Landsat 8 OLI 4 4 February 2017 37 183 0.11 Landsat 8 OLI 5 4 February 2017 39 183 0.13 Landsat 8 OLI 6 19 February 2017 37 184 1.00 Landsat 8 OLI 7 19 February 2017 38 184 0.00

**Data Source Resolution** Landsat satellite imagery USGS 30 m DEM USGS 30 m Population density GHSL 250 m Road network Diva GIS / Land surface temperature MODIS 0.25° Rainfall MODIS 0.25° Net primary productivity MODIS 0.1° NDVI MODIS 0.1° Air quality (CO, NO2) MODIS 0.25°

*Urban Planning Using a Geospatial Approach: A Case Study of Libya*

*DOI: http://dx.doi.org/10.5772/intechopen.86355*

Four preprocessing steps were performed on the Landsat satellite images: (i) Pan-sharpening using a fusion of the panchromatic and multispectral bands for the enhancement of the spatial resolution of multispectral band; (ii) atmospheric correction, which is applied to correct the atmospheric distortion by retrieving surface reflectance and engage topographic correction as well as adjacency effect correction; (iii) radiometric correction, which converts radiance values to the pure surface reflectance to enhance image capability and contrast; and (iv) mosaicking to create one seamless image coverage of the area for effective and efficient processing [22]. The MODIS source data was preprocessed using MODIS Conversion Tool Kit (MCTK). Note that the spatial resolution of the MODIS dataset varied according to the source. However, during the preprocessing, they were resampled to 30 m to

In this study, we considered 17 critical urban conditioning factors for selecting the most suitable city or cities for sustainable urban development. The factors are

effective and efficient processing (**Figure 1d**).

*Information of the datasets used in the research.*

match the DEM and Landsat resolutions.

**2.3 Urban conditioning factor dataset**

**2.2 Data preprocessing**

*Information of the Landsat images.*

**Table 1.**

**Table 2.**

**243**

Al Hizam Al Akhdar (**Figure 1**). Libya is geographically bounded between 20°00<sup>0</sup> 00″ E and 23°30<sup>0</sup> <sup>00</sup>″ E and 31°00<sup>0</sup> <sup>00</sup>″ N and 33°00<sup>0</sup> <sup>00</sup>″ N. The climate in Libya is categorized by hot and dry summers with high temperatures. The mean annual temperature in the coastal region ranges from 14.2°C (Shahat) to 21.0°C (Tripoli Airport) and at stations in the interior region (inland) between 21.3°C (Al Qaryat) and (Ghat) 23.4°C (1945–2009). Libya is one of the driest countries in the world with mean annual rainfall along the Libyan coast ranging between 140 and 550 mm and rarely exceeding 50 mm in the interior regions (1945–2010). December and January are the wettest months with 6 months (October–March) receiving 87.1% of the total annual precipitation. The majority of rainfall occurs in the winter season with the rainy season beginning in September-October and ends in March-April [21].

#### **2.1 Data preparation**

The data used in this study include Landsat satellite imagery acquired in the year 2017 with 15 m resolution panchromatic and 30 m resolution multispectral, Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) downloaded from USGS data archive with 30 m resolution, population density map obtained from GHSL with 250 m resolution, road network map from Diva-GIS, and MODIS satellite imagery from where the land surface temperature with 0.25° resolution was derived. Other data include rainfall data at 0.25°, net primary productivity (NPP) at 0.1°, NDVI at 0.1°, and air quality (CO, NO2) at 0.25° resolution (**Table 1**). Details of the Landsat data are presented in **Table 2**. Seven set of images with overlapping areas were acquired between 4 February 2017 and 1 March 2017. In addition, the

*Urban Planning Using a Geospatial Approach: A Case Study of Libya DOI: http://dx.doi.org/10.5772/intechopen.86355*


#### **Table 1.**

*Information of the datasets used in the research.*


#### **Table 2.**

Al Hizam Al Akhdar (**Figure 1**). Libya is geographically bounded between 20°00<sup>0</sup>

rized by hot and dry summers with high temperatures. The mean annual temperature in the coastal region ranges from 14.2°C (Shahat) to 21.0°C (Tripoli Airport) and at stations in the interior region (inland) between 21.3°C (Al Qaryat) and (Ghat) 23.4°C (1945–2009). Libya is one of the driest countries in the world with mean annual rainfall along the Libyan coast ranging between 140 and 550 mm and rarely exceeding 50 mm in the interior regions (1945–2010). December and January are the wettest months with 6 months (October–March) receiving 87.1% of the total annual precipitation. The majority of rainfall occurs in the winter season with the rainy season

*(a) Map of Libya with northern part highlighted, (b) the location of the urban area, (c) the road networks in*

The data used in this study include Landsat satellite imagery acquired in the year 2017 with 15 m resolution panchromatic and 30 m resolution multispectral, Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) downloaded from USGS data archive with 30 m resolution, population density map obtained from GHSL with 250 m resolution, road network map from Diva-GIS, and MODIS satellite imagery from where the land surface temperature with 0.25° resolution was derived. Other data include rainfall data at 0.25°, net primary productivity (NPP) at 0.1°, NDVI at 0.1°, and air quality (CO, NO2) at 0.25° resolution (**Table 1**). Details of the Landsat data are presented in **Table 2**. Seven set of images with overlapping areas were acquired between 4 February 2017 and 1 March 2017. In addition, the

<sup>00</sup>″ N and 33°00<sup>0</sup>

beginning in September-October and ends in March-April [21].

E and 23°30<sup>0</sup>

**Figure 1.**

**2.1 Data preparation**

**242**

<sup>00</sup>″ E and 31°00<sup>0</sup>

*the study area, and (d) mosaicked Landsat images.*

*Sustainability in Urban Planning and Design*

00″

<sup>00</sup>″ N. The climate in Libya is catego-

*Information of the Landsat images.*

highest cloud cover was 1.03%, which does not pose a problem for land use information extraction from the study area. Since the images have overlapping areas, they were preprocessed and mosaicked to create one seamless image of the area for effective and efficient processing (**Figure 1d**).

#### **2.2 Data preprocessing**

Four preprocessing steps were performed on the Landsat satellite images: (i) Pan-sharpening using a fusion of the panchromatic and multispectral bands for the enhancement of the spatial resolution of multispectral band; (ii) atmospheric correction, which is applied to correct the atmospheric distortion by retrieving surface reflectance and engage topographic correction as well as adjacency effect correction; (iii) radiometric correction, which converts radiance values to the pure surface reflectance to enhance image capability and contrast; and (iv) mosaicking to create one seamless image coverage of the area for effective and efficient processing [22]. The MODIS source data was preprocessed using MODIS Conversion Tool Kit (MCTK). Note that the spatial resolution of the MODIS dataset varied according to the source. However, during the preprocessing, they were resampled to 30 m to match the DEM and Landsat resolutions.

#### **2.3 Urban conditioning factor dataset**

In this study, we considered 17 critical urban conditioning factors for selecting the most suitable city or cities for sustainable urban development. The factors are

grouped into five main categories: (i) topography, (ii) land use and infrastructure, (iii) demography and climate, (iv) vegetation, and (v) air quality.

data [26]. It basically extracts the urban areas where there is an upper reflectance in the short-wave infrared band associated to the near-infrared band. The accuracy of built-up areas extracted using NDBI is reported to be around 93% [27, 28]. We

*NDBI* <sup>¼</sup> *SWIR* � *NIR*

*SWIR* <sup>þ</sup> *NIR* (1)

calculate the NDBI (Eq. (1)) based on the work in [27]:

*Urban Planning Using a Geospatial Approach: A Case Study of Libya*

*DOI: http://dx.doi.org/10.5772/intechopen.86355*

**245**

## *2.3.1 Topography*

Topography is a very important consideration for urban development projects [23]. For this study, altitude and slope are the two main factors related to topography. Altitude is important for citing facility because it affects the living conditions as well as breathing behavior. The collected DEM shows that the study area is between 4 and 865 m above mean sea level (**Figure 2a**). The slope factor, which ranges from 0 to 14° (can be classified as almost flat), was also generated (**Figure 2b**). Such data is important when estimating cost. For example, any increase in slope will increase the cost of facility installation and maintenance since moving workers, transport vehicles, and machineries will be more difficult (i.e., up and down a slope). Low slope areas also may incur undesirable cost, in the instance of weather anomalies such as dust/sand storms.

#### *2.3.2 Land use and infrastructure*

Land use and infrastructure are also important considerations for urban projects. Land use information can show human activity patterns, whereas infrastructure can indicate development status in a particular city. The land use of the study area was derived from Landsat images and refined based on Google maps (**Figure 2c**). In this study we applied the SVM classifier, which was based on object-based image analysis (OBIA) using the ENVI 5.3 software. Training sites for the SVM were collected form all land use classes by stratified random method (i.e., at least 80 sample points for each class) [24]. The area contains five main land use types: (i) irrigated crops, (ii) vegetation, (iii) artificial areas, (iv) bare lands, and (v) waterbodies. Most parts of the study area were bare land (desert), which were predominantly located in the middle and southern parts of the study area. The northern part mostly comprised of irrigated crops and artificial areas, specifically man-made features and urban areas.

Road networks play an important role in the country's economy, serving the people by linking main cities to industrial and commercial sites. In this study, three types of roads, namely, main routes, secondary routes, and trail routes (**Figure 2d–f**), were considered as factors for city selection. The northern part of the city is supported by main routes (**Figure 2d**). These roads mainly link other cities to Benghazi, which support Benghazi city itself. Main routes span a significant number of kilometers within the study area. The study area also contains several kilometers of secondary routes (**Figure 2e**). Unlike main routes, secondary routes are found in most parts of the study area and in different cities including Benghazi. Secondary routes mainly support transportation of goods and are used for civil construction projects. Finally, trail routes support the rural areas, mainly for transportation of agricultural produce to the markets. The class of roads plays a vital role in selecting a city for development according to the available budget. Cities that can support more people will normally be prioritized for development projects.

Another important factor related to infrastructure is the percentage of built-up areas in a particular city. This is important because cities with many built-up areas indicate little or no space for new projects. On the contrary, cities with fewer builtup areas mean that they are more suitable for new developmental projects. The Normalized Difference Built-up Index (NDBI), which is a quantity of the intensity of urban area from satellite images, was used in this study [25]. The NDBI was initially established regarding the ratio of bands 4 and 5 of TM sensor. However, the NDBI can be adopted on Landsat-8 data or even any multispectral sensor

*Urban Planning Using a Geospatial Approach: A Case Study of Libya DOI: http://dx.doi.org/10.5772/intechopen.86355*

grouped into five main categories: (i) topography, (ii) land use and infrastructure,

Topography is a very important consideration for urban development projects [23]. For this study, altitude and slope are the two main factors related to topography. Altitude is important for citing facility because it affects the living conditions as well as breathing behavior. The collected DEM shows that the study area is between 4 and 865 m above mean sea level (**Figure 2a**). The slope factor, which

Land use and infrastructure are also important considerations for urban projects. Land use information can show human activity patterns, whereas infrastructure can indicate development status in a particular city. The land use of the study area was derived from Landsat images and refined based on Google maps (**Figure 2c**). In this study we applied the SVM classifier, which was based on object-based image analysis (OBIA) using the ENVI 5.3 software. Training sites for the SVM were collected form all land use classes by stratified random method (i.e., at least 80 sample points for each class) [24]. The area contains five main land use types: (i) irrigated crops, (ii) vegetation, (iii) artificial areas, (iv) bare lands, and (v) waterbodies. Most parts of the study area were bare land (desert), which were predominantly located in the middle and southern parts of the study area. The northern part mostly comprised of irrigated crops and artificial areas, specifically man-made features and urban areas. Road networks play an important role in the country's economy, serving the people by linking main cities to industrial and commercial sites. In this study, three types of roads, namely, main routes, secondary routes, and trail routes (**Figure 2d–f**), were considered as factors for city selection. The northern part of the city is supported by main routes (**Figure 2d**). These roads mainly link other cities to Benghazi, which support Benghazi city itself. Main routes span a significant number of kilometers within the study area. The study area also contains several kilometers of secondary routes (**Figure 2e**). Unlike main routes, secondary routes are found in most parts of the study area and in different cities including Benghazi. Secondary routes mainly support transportation of goods and are used for civil construction projects. Finally, trail routes support the rural areas, mainly for transportation of agricultural produce to the markets. The class of roads plays a vital role in selecting a city for development according to the available budget. Cities that can

support more people will normally be prioritized for development projects.

Another important factor related to infrastructure is the percentage of built-up areas in a particular city. This is important because cities with many built-up areas indicate little or no space for new projects. On the contrary, cities with fewer builtup areas mean that they are more suitable for new developmental projects. The Normalized Difference Built-up Index (NDBI), which is a quantity of the intensity of urban area from satellite images, was used in this study [25]. The NDBI was initially established regarding the ratio of bands 4 and 5 of TM sensor. However, the NDBI can be adopted on Landsat-8 data or even any multispectral sensor

(iii) demography and climate, (iv) vegetation, and (v) air quality.

ranges from 0 to 14° (can be classified as almost flat), was also generated (**Figure 2b**). Such data is important when estimating cost. For example, any increase in slope will increase the cost of facility installation and maintenance since moving workers, transport vehicles, and machineries will be more difficult (i.e., up and down a slope). Low slope areas also may incur undesirable cost, in the instance

of weather anomalies such as dust/sand storms.

*Sustainability in Urban Planning and Design*

*2.3.2 Land use and infrastructure*

**244**

*2.3.1 Topography*

data [26]. It basically extracts the urban areas where there is an upper reflectance in the short-wave infrared band associated to the near-infrared band. The accuracy of built-up areas extracted using NDBI is reported to be around 93% [27, 28]. We calculate the NDBI (Eq. (1)) based on the work in [27]:

$$NDBII = \frac{SWIR - NIR}{SWIR + NIR} \tag{1}$$

built-up area is found in Benghazi city (>45%). Some cities though, such as Al Marj and Darnah, have very small of built-up areas that are not detectable through

An increase in a city's population often leads to an increase in urbanization. Moreover, if the population increase is rapid, urbanization often happens randomly. This can be a major problem for most cities in a developing country. However, proper planning and effective decision-making can mitigate this problem. In this study, the population density (**Figure 2i**) was analyzed. The analysis results indicate that the northern part (mostly around Benghazi city) is most populated with a

Climate is a factor that also influences the selection of cities for developmental projects. Land surface temperature (LST) and rainfall are two factors considered in this work (**Figures 2j** and **3k**). The LST map shows that the southern part of the study area (mostly desert with no vegetation) has higher surface temperature compared to the northern parts. Another observation from the map reveals that Benghazi has slightly higher temperature than other urbanized areas. In arid regions, people often prefer to settle in areas with low temperature. The average day-night temperature ranges from 11° to 20° Centigrade. High temperatures are also

observed in the west-southern part, whereas the lowest temperature is found in the

Normalized difference vegetation index (NDVI) is an indicator derived from remote sensing satellite data. It is mostly used to monitor vegetation cover over any area on the planet. It serves as a good indicator for vegetation cover of the study area. The presence of abundant vegetation is able to lower the local temperature as well as reduces the negative effects of noise and air pollutants. In the study area, the

Larger amounts of vegetation can indicate higher vegetation productivity. Hav-

northern part has higher NDVI compared to the south (**Figure 2l**).

ing higher vegetation productivity helps asses the net primary productivity (**Figure 2m**). Plant productivity plays a major role in the global carbon cycle by absorbing some of the carbon dioxide released through coal, oil, and other fossilfuel burning. Large NPP values are found in the southern part of the study area.

Rainfall, which is another climate factor, is also considered in deciding the location of settlement and development. This is because rainfall frequency and intensity affect the dryness of the cities, the local climate system, as well as agriculture activities. **Figure 2k** presents the rainfall intensity of the study area for year 2016 where minimum and maximum rainfall intensities were 48 and 1119 mm per month, respectively. The central part of the area has less amount of rainfall

are as far as 400 km away from Benghazi) are also covered.

*Urban Planning Using a Geospatial Approach: A Case Study of Libya*

*DOI: http://dx.doi.org/10.5772/intechopen.86355*

density of 669 people per 250 m cell of raster data.

northern part of Al Jabal Al Akhdar cities.

compared to other areas.

*2.3.4 Vegetation*

**247**

Besides infrastructure factors, distance to the city is also a critical factor. Preferably, a city's location should be as near as possible to the capital or large cities such as Benghazi. This is because it facilitates ease of access to better business opportunities and education. Therefore, in this work, the distance to Benghazi city is one of the important parameters. Specifically, the desired distance to the city should range from 0 to 600 km (**Figure 2g**) so that cities such as Darnah and Al Qubbah (which

satellite data.

*2.3.3 Demography and climate*

#### **Figure 2.**

*Elevation criteria: (a) altitude, (b) slope, (c) land use, (d) distance to the primary routes, (e) distance to the secondary routes, (f) distance to the trails, (g) distance to the Benghazi city, (h) percent of urban areas, (i) population density, (j) LST, (k) rainfall, (l) NDVI, (m) NPP product, (n) CO concentrations, (o) NO2 concentrations.*

*SWIR* is the short-wave infrared band ranging from 1.57 to 1.65 *μm*. *NIR* is the near-infrared band in the range of 0.85–0.88 *μm*. **Figure 2h** shows the percentage of built-up areas calculated for each district considered in this work. The largest

*Urban Planning Using a Geospatial Approach: A Case Study of Libya DOI: http://dx.doi.org/10.5772/intechopen.86355*

built-up area is found in Benghazi city (>45%). Some cities though, such as Al Marj and Darnah, have very small of built-up areas that are not detectable through satellite data.

Besides infrastructure factors, distance to the city is also a critical factor. Preferably, a city's location should be as near as possible to the capital or large cities such as Benghazi. This is because it facilitates ease of access to better business opportunities and education. Therefore, in this work, the distance to Benghazi city is one of the important parameters. Specifically, the desired distance to the city should range from 0 to 600 km (**Figure 2g**) so that cities such as Darnah and Al Qubbah (which are as far as 400 km away from Benghazi) are also covered.

#### *2.3.3 Demography and climate*

An increase in a city's population often leads to an increase in urbanization. Moreover, if the population increase is rapid, urbanization often happens randomly. This can be a major problem for most cities in a developing country. However, proper planning and effective decision-making can mitigate this problem. In this study, the population density (**Figure 2i**) was analyzed. The analysis results indicate that the northern part (mostly around Benghazi city) is most populated with a density of 669 people per 250 m cell of raster data.

Climate is a factor that also influences the selection of cities for developmental projects. Land surface temperature (LST) and rainfall are two factors considered in this work (**Figures 2j** and **3k**). The LST map shows that the southern part of the study area (mostly desert with no vegetation) has higher surface temperature compared to the northern parts. Another observation from the map reveals that Benghazi has slightly higher temperature than other urbanized areas. In arid regions, people often prefer to settle in areas with low temperature. The average day-night temperature ranges from 11° to 20° Centigrade. High temperatures are also observed in the west-southern part, whereas the lowest temperature is found in the northern part of Al Jabal Al Akhdar cities.

Rainfall, which is another climate factor, is also considered in deciding the location of settlement and development. This is because rainfall frequency and intensity affect the dryness of the cities, the local climate system, as well as agriculture activities. **Figure 2k** presents the rainfall intensity of the study area for year 2016 where minimum and maximum rainfall intensities were 48 and 1119 mm per month, respectively. The central part of the area has less amount of rainfall compared to other areas.

#### *2.3.4 Vegetation*

Normalized difference vegetation index (NDVI) is an indicator derived from remote sensing satellite data. It is mostly used to monitor vegetation cover over any area on the planet. It serves as a good indicator for vegetation cover of the study area. The presence of abundant vegetation is able to lower the local temperature as well as reduces the negative effects of noise and air pollutants. In the study area, the northern part has higher NDVI compared to the south (**Figure 2l**).

Larger amounts of vegetation can indicate higher vegetation productivity. Having higher vegetation productivity helps asses the net primary productivity (**Figure 2m**). Plant productivity plays a major role in the global carbon cycle by absorbing some of the carbon dioxide released through coal, oil, and other fossilfuel burning. Large NPP values are found in the southern part of the study area.

*SWIR* is the short-wave infrared band ranging from 1.57 to 1.65 *μm*. *NIR* is the near-infrared band in the range of 0.85–0.88 *μm*. **Figure 2h** shows the percentage of built-up areas calculated for each district considered in this work. The largest

*Elevation criteria: (a) altitude, (b) slope, (c) land use, (d) distance to the primary routes, (e) distance to the secondary routes, (f) distance to the trails, (g) distance to the Benghazi city, (h) percent of urban areas, (i) population density, (j) LST, (k) rainfall, (l) NDVI, (m) NPP product, (n) CO concentrations, (o) NO2*

**Figure 2.**

**246**

*concentrations.*

*Sustainability in Urban Planning and Design*

#### *2.3.5 Air quality*

Air quality directly affects the environment and consequently people's health. In this work, we have considered the CO and NO2 (**Figure 2n** and **o**) air quality indicators. In 2016, higher CO and NO2 levels were measured in the southern part of Benghazi. Benghazi city also recorded high levels of these gasses for the year under investigation. The air quality data was extracted from the MODIS source with a resolution of 0.25°. We utilized the ENVI 5.3 software to process the MODIS imagery. However, in order to prepare unprocessed MODIS satellite images for analysis, they must firstly be converted into ENVI format. This was done using the MODIS Conversion Tool Kit.

machine (SVM) algorithm was used. Although the SVM is a relatively simple binary classifier, it has very good generalization capabilities if properly trained [31, 32]. Several other digital data such as DEM and population density were also obtained from various online sources. The factors used as described in the previous section are widely reported in the literature for selecting urban projects or relevant projects. Fuzzy overlay (FO) analysis was carried out to determine the importance of each parameter to achieving the goal of the study. The SVM classifier was further applied to refine the results obtained from the FO model. Finally, the cities were sorted according to their importance by applying the TOPSIS model on the results

*Urban Planning Using a Geospatial Approach: A Case Study of Libya*

Fuzzy overlay analysis is based on the fuzzy set theory that relies on membership relationship of events to define specific sets or classes [33]. Operationally, FO is similar to overlay analysis but differs in the reclassified values and results from the combination of multiple criteria. It involves problem definition, partitioning into sub-models and determining the significant layers. FO transforms the data to a common scale and defines the likelihood of the data belonging to a specific class, for example, slope values being transformed into the probability of fitting into the favorable suitability set based on a scale of 0 to 1, expressed in terms of membership [34]. Input raster are not weighted in FO since the transformed values indicate the possibility of membership rather than using ratio scale as with weighted overlay and weighted sum. The equation using fuzzy Gaussian function can be given as [35]

*μ*ð Þ¼ *x e*

�*f* <sup>∗</sup> *<sup>x</sup>*�*<sup>f</sup>* ð Þ<sup>2</sup> <sup>2</sup>

The inputs *fi* and *f* <sup>2</sup> are the spread and the midpoint, respectively. Midpoint can be a user-defined value with a fuzzy membership of 1. The default is the midpoint of the range of values of the input raster. Spread defines the membership of the Gaussian function. It generally ranges from 0.01 to 1. Increasing the spread causes the fuzzy membership curve to become steeper. Fuzzy overlay analysis quantifies the possibilities of each cell or location to a specified set based on membership

As previously mentioned, the results of FO are refined using the SVM, which develops a linear regression between suitability status and criteria factors. SVM aims to determine an optimal separating hyperplane (maximizing the margin width) between two classes in feature space [36]. The training points near the hyperplane are called support vectors and are utilized for classification once the decision line/surface is obtained. The separating hyperplane is found as follows:

where *w* is the cofficienct vector that defines the hyperplane orientation in the feature space, *b* is the offset of the hyperplane from the origin, and *ε<sup>i</sup>* is the positive slack variables. The optimal hyperplane is found by solving the following optimiza-

*αiyi* ¼ 0*,* 0≤*α<sup>i</sup>* ≤*C*

*yi*

Minimize∑

*n i*¼1

*subject*∑ *n i*¼1

*<sup>α</sup><sup>i</sup>* � <sup>1</sup> 2 ∑ *n i*¼1 ∑ *n j*¼1 *αiαjyi*

*<sup>i</sup>* (2)

ð Þ *w* � *xi* þ *b* ≥1 � *ε<sup>i</sup>* (3)

*yj xixj* 

(4)

of the SVM.

value.

**249**

tion problem [36, 37]:

**3.1 Fuzzy overlay and TOPSIS models**

*DOI: http://dx.doi.org/10.5772/intechopen.86355*
