**The steps of the fuzzy AHP technique using Chang’s method can be given as follows: **

**STEP 1: Draw the hierarchical chart**

**STEP 2: Define fuzzy numbers for performing the pair-wise comparisons**

**STEP 3: Create the pair-wise comparison matrix **** using fuzzy numbers**

The pair-wise comparison matrix can be expressed as follows**:**

If there are several experts, elements of a complete pairwise comparison matrix used in the fuzzy AHP method is a triangular fuzzy number where the first component (l) is the least comments, the second component (m) is the mean of numbers and the third component (u) is the maximum number.

**STEP 4: Calculate **** **** for each row of the pair-wise comparison matrix**

can be calculated using the following formula:

Where i represents the row number and j denotes the column number. In the formula, is triangular fuzzy numbers of pairwise comparison matrices. The values of and can be calculated by using the following formulas, respectively:

In the above formulas,, and are the first, second, and third components of the fuzzy numbers, respectively.

**STEP 5: Compute the magnitude of **** with respect to each other**

In general, if and are two triangular fuzzy numbers, then, as shown in the following figure, the magnitude of with respect to can be defined as follows:

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On the other hand, the magnitude of a triangular fuzzy number from k as another triangular fuzzy number can be obtained by the following formula:

**STEP 6: Compute the weight of the criteria and alternatives in the pair-wise comparison matrix**

The following formula can be used for this purpose:

Therefore, the unnormalized weight vector can be given as follows:

* *

**STEP 7: Calculate the final weight vector**

To calculate the final weight vector, the calculated weight vector in the previous step should be normalized, then :

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