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ANALYTIC HIERARCHY PROCESS
(AHP)
Prof. Ta Chung Chu
Student: Nguyen Khoa Tu Uyen_M977Z215
1. INTRODUCTION
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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
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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)
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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)

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