**7. Results and discussions**

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 cri-

activity (j), then (j)has the reciprocal value when compared with (i)

If activity (i) has one of the above nonzero numbers assigned to it when compared with

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

The consistency index (CI) for each matrix can be expressed as:CI <sup>=</sup> (λmax ‐n)/(<sup>n</sup> <sup>−</sup> 1); Where λmaxis

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

A multicriteria evaluation consists of combining a set of criteria (constraints and factors) to build a single suitability map according to a specific category (set of factors). One of the most common procedures for aggregating data is the weighted linear combination (WLC) [19].

WLC is a technique based on the concept of a weighted average in which continuous criteria are standardized to a common numeric range, and then combined by means of a weighted

average to produce a continuous mapping of suitability [13].

teria. The method uses a scale with values range from 1 to 9, illustrated in **Table 2**.

the principal eigenvalue of the judgment matrix and n is its order Saaty [18].

index (RI).

resultant weights are applied.

**Intensity of importance Definition** 1 Equal importance

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

Reciprocals of above

non zero

 Weak importance of one over another Essential or strong importance Demonstrated importance Absolute importance

2,4,6,8 Intermediate values between adjacent judgments the two

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

**6. MCE using WLC method**
