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ANALYTIC HIERARCHY PROCESS
(AHP)
Prof. Ta Chung Chu
Student: Nguyen Khoa Tu Uyen_M977Z215
1. INTRODUCTION
The Analytic Hierarchy Process (AHP) was devised by
Saaty (1980, 1994)
It is a useful approach to solve complex decision problems.
It prioritizes the relative importance of a list of criteria
through pair-wise comparisons amongst the factors by
relevant experts using a nine-point scale.
Buckley (1985) incorporated the fuzzy theory into the
AHP, called the Fuzzy Analytic Hierarchy Process
(FAHP). It generalizes the calculation of the consistent
ratio (CR) into a fuzzy matrix.
2. THE PROCEDURE OF FAHP
Step 1: Construct fuzzy pair-wise comparison matrices.
Through expert questionnaires, each expert is asked to assign
linguistic terms by TFN (as shown in Table 1 and Fig. 1) to the
pairwise comparisons among all criteria in the dimensions of a
hierarchy system. The result of the comparisons is constructed
as fuzzy pairwise comparison matrices
as shown in Eq.
(1).
Step 2: Examine the consistency of the fuzzy pairwise
comparison matrices
According to the research of Buckley (1985), it proves that if
is a positive reciprocal matrix then
is a fuzzy positive
reciprocal matrix. That is, if the result of the comparisons of
is consistent, then it can imply that the result of the
comparisons of
is also consistent.
(1)
Step 3: Compute the fuzzy geometric mean for each criterion.
The geometric technique is used to calculate the geometric
mean
of the fuzzy comparison values of criterion i to each
criterion, as shown in Eq. (2), where
is a fuzzy value of
the pair-wise comparison of criterion i to criterion n (Buckley,
1985)
(2)
Step 4: Compute the fuzzy weights by normalization.
The fuzzy weight of the ith criterion
, can be derived as
Eq.(3), where
is denoted as
by a TFN
and Lwi , Mwi , and Uwi represent the lower, middle and upper
values of the fuzzy weight of the ith criterion.
(3)