**5. Weighting factors for aggregation**

all the thematic maps were transformed on raster grid to be used by Idrisi software. A raster

given factor. All the factors influenced were standardized and weighed and then combined

• The Exclusion of restricted areas for landfill siting. The constraints based on the Boolean criteria were used to differentiate areas that can be considered suitable for a waste disposal

• The factors were standardized to a continuous scale of suitability from 0 (least suitable) to 10 (most suitable) in a GIS environment by fuzzy membership functions, then weighted

The site selection process is implemented in the following steps:

**Table 1.** Hierarchical structure for the selection of the MSW landfill site.

and combined using the AHP methods.

site from those that cannot be considered suitable under any conditions

was generated. Each cell is considered as a homogenous unit for any

grid cell of 100 × 100 m2

**Level 1 Goal**

Landfill suitability **Level 2**

**Decision factors**

**Level 3 Subfactors**

Elevation \* Slope \* Distance from coastal zone \*

Distance from water supply (reservoirs, wells, boreholes,

Distance from irrigation

Olfactory and sonorous

Distance from residential

Environment Land use \* \*

Social Proximity to dense population \*

Economic Proximity to roads \* \* Proximity to building

Distance from wetlands \* Distance from rivers \*

Distance from protected areas \*

Geology Soil permeability \*

74 Fuzzy Logic Based in Optimization Methods and Control Systems and Its Applications

Hydro/Hydrogeology Depth to ground water table \*

springs)

canals

impacts

areas

materials

**Exclusion criteria**

\*

\*

\*

\*

\*

**Appreciation criteria**

using the AHP methods.

The purpose of criterion weighting is to express the importance of each criterion relative to other criteria. One of the techniques that can be used in assigning weights is Pairwise Comparisons (that characterizes analytic hierarchy process: AHP, developed by Saaty [18]; it determines accurate relative weights of indicators by allowing to divide the complex decision problem into a series of one-on-one judgments regarding the significance of each criterion relative to the others.


The suitability index for a site is the sum of the products of the standardized score for each criterion multiplied by the weight of each criterion, the following equation is given by Eastman

> i=1 n wi xi

number of criteria. As the sum of the weights is constrained to one, the final combined esti-

In Tunisia, there is not a Solid Waste Control Regulations for disposal site. Hence, criteria were selected according the MSW landfill siting guidelines of the countries legislation, extensive literature review, [1–4, 7, 9, 11, 13] assessment via questionnaire; availability of the data

In this study, 13 constraints criteria such as: (1) Soil permeability, (2) Elevation, (3) Slope, (4) Distance from coastal zone,(5) Depth to ground water table, (6) Distance from water supply (reservoirs, wells, boreholes, springs), (7) Distance from wetlands, (8) Distance from rivers, (9) Distance from irrigation canals, (10) Land use, (11) Proximity to roads, (12) Distance from protected areas, and (13) Distance from residential areas were selected for the computation

**Figure 2** shows the maps layers of all the constraints criteria after buffering and restriction.

The next process is to further examine the suitable areas for landfill. Factor criteria were used

Land use is important for resolving public conflicts over the acceptance of unwanted facility siting [4]. **Table 4** shows the membership values assigned to all categories used in the analysis

based on results of investigations with experts (agronomist, environmentalists…).

process. The buffer zones in the different constraint layers are listed in **Table 3**.

, w2

,…,xn are the standardized scores of the criteria i and n is the total

An Integrated Multicriteria and Fuzzy Logic Approach for Municipal Solid Waste Landfill Siting

,…,wn are the weights of the criteria con-

http://dx.doi.org/10.5772/intechopen.75161

77

[20]:

S = ∑

where S is the suitability index for area i; w1

mate is presented on the same scale.

**7. Results and discussions**

*7.1.1. Exclusive criteria (constraints)*

*7.1.2. Appreciation criteria (factors)*

*7.1.3. Environmental factor*

*7.1.3.1. Land use*

in order to further evaluate those areas.

**7.1. Criteria description and application**

, x2

strained to sum to 1; x1

and local expert.

**Table 2.** The comparison scale in AHP Saaty [14].

The pairwise comparison involves three tasks: (1) developing a comparison matrix at each level of the hierarchy initial from the second level and functioning down, (2) computing the relative weights for each element of the hierarchy and (3) estimating the consistency ratio to check the consistency of the judgment [19]. In the AHP weight can be derived by taking the principal eigenvector of a square reciprocal matrix of pair-wise comparisons between the criteria. The method uses a scale with values range from 1 to 9, illustrated in **Table 2**.

The consistency ratio is one of the very important aspects of the AHP theory. It allows us to assess the overall consistency of all pairwise comparison judgments provided by the decision makers in the form of pairwise comparison judgment matrices. More formally, the consistency ratio (CR) is calculated through dividing the consistency index (CI) by the randomized index (RI).

The consistency index (CI) for each matrix can be expressed as:CI <sup>=</sup> (λmax ‐n)/(<sup>n</sup> <sup>−</sup> 1); Where λmaxis the principal eigenvalue of the judgment matrix and n is its order Saaty [18].

Then, the consistency ratio (CR) is defined as follows: CR = CI/RI; Where RI is the random index and depends on the number of elements being compared Saaty [18]. If CR < 0.10, the ratio indicates a reasonable level of consistency in the pairwise comparison; however, if CR ≥ 0.10, it indicates inconsistent judgments [18]. Once the satisfactory CR is obtained, the resultant weights are applied.
