Selection of Water Quality Monitoring Stations - Water Quality Management: Assessment and Interpretation - page 9

2.3.2 Assessment of Weighting (Wj) for Attributes

In the majority of MCDM problems, particularly the part of MADM, it is essential
to be acquainted with the relative signi cance of existing attributes, considering the

sum of them should be equal to 1, and this relative signi

cance assesses the
preference rank of each attribute compared with other attributes for speci ed

decision. There are various methods of weighting in MCDM. Considering the
experts ' opinions and the existing conditions, it is selected and weighted parameters
that have a speci

cance in
special consumptions and also parameters which are given a higher worth for water
quality attributes.
The

c signi cance in the standard and have a high signi

final stage of decision is ranking of stations using Simple Additives
weighting method (SAW).
In the SAW method vector w (weights of signi

cant attributes that obtained in
previous) is assumed and suitable alternative A* is calculated as follows:
A ¼ A i j max P w i r ij P w j ð 2 : 7 Þ

And if P w j ¼ 1:

n o

A ¼ A i j max X w i r ij

ð 2 : 8 Þ

Final weights that were obtained in the previous part are used in this stage and
multiplied to equalized and dimensionless values of MADM matrix, and are the cal-
culated sum of the parameters in each line. Therefore, for each station, a number was
obtained that can be our selection attribute and based on that the stations were speci ed.

2.4 Dynamic Programming Approach (DPA) Method

The DPA is one of most applicable technique which nowadays is applied for
modeling of operation systems. The DPA is a method for solving the problems joint
with the Multi-stage Decision. In this method concerning the characteristic of
staging the problem, we solve the problem with n staging and single variable
instead of solving the problem with n variables.

2.4.1 The DPA Theory

At the first stage, reduction of the network is achieved by dividing river catchment

area to N (K = 1, 2, … N) Primary basin. This division should not be according to the