Fuzzy AHP (chang) steps

Step1.The fuzzy synthetic extent value (Si) with respect to the ith criterion is defined as equation 1 .

To obtain equation 2;

perform the “fuzzy addition operation” of m extent analysis values for a particular matrix given in equation 3 below, at the end step of calculation, new (l, m, u) set is obtained and used for the next:

Where l is the lower limit value, m is the most promising value and u is the upper limit value.
and to obtain equation 4;

perform the “fuzzy addition operation” of   fuzzy ahp - 5    values give as equation 5:

and then compute the inverse of the vector in the equation (5) equation (6) is then obtained such that

Step 2. The degree of possibility of

fuzzy ahp 8 is defined as equation 7: 

and x and y are the values on the axis of membership function of each criterion. This expression can be equivalently written as given in equation 8 below:

where d is the highest intersection point  and  (see Figure 1)

To compare M1 and M2; we need both the values of V(M2≥ M1) and V(M1≥M2):

Step 3. The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers

can be defined by

Assume that equation 9 is

For k = 1, 2, 3, 4, 5, ……, n; k ≠ i. Then the weight vector is given by equation 10:

Step 4. Via normalization, the normalized weight vectors are given in equation 11:

Where W is non-fuzzy numbers.