The topic under discussion has not only
theoretical value - it is significant primarily in a
practical sense. It should be noted that in this article
the task of multi-criteria selection of objects for
research is considered in the context of the problem
of identification of potentially depressed rural areas
in the conditions of Northern Kazakhstan.
However, the developed methodological techniques
and procedures can be used to solve other similar
problems.
2 Materials and Methods
Currently, there are two approaches to solving this
problem in the literature. Each of them is based on
ideas that are quite disputable. The first approach is
based on the formation of some ideal reference
options; the best values of the criteria are taken as
reference options [11]. Then the distances between
the values of the criteria in each of the considered
options and their corresponding values of the
reference option are measured. Further, the
found distances are "normalized", that is, they are
reduced to a relative indicator by dividing the
distances by the corresponding reference values:
, (1)
where the normalized distance between the
value of the criterion and its reference value
according to the option.
The option that has the smallest sum of the
absolute values of the normalized distances is
considered to be the closest to the “etalon” and
therefore is considered optimal. The methodology
finds its application in solving multi-criteria tasks
in which (a) the search for the best (most
promising) alternatives is conducted and (b)
different criteria taken into account in the selection
process have equal priorities.
Another approach to solving the problems of
multi-criteria selection of the best option is called
the analytical hierarchical process; the method
became famous abroad, mainly in the United States
of America (the calculation procedure is given in.
The method allows us to find a solution to the
problem in several stages. At the first step, the
weights of the criteria are evaluated. To do this, a
matrix of numbers is constructed, representing
pairwise estimates of the preference of criteria
relative to each other. Moreover, the weights are
calculated so that in total they turn out to be equal
to one. Further, numerical estimates of alternatives
relative to each of the criteria are given on a certain
scale. Then the estimates of alternatives relative to
each criterion are "normalized" so that for each
criterion in total they give one. At the third stage,
the sum of normalized estimates weighted by the
importance of the criteria (found at the first stage)
is calculated for each alternative. Alternatives are
ranked according to weighted sums of estimates.
The key feature of the methodology is the
calculation of weights of criteria and "normalized"
estimates of alternatives based on an arbitrarily
taken point scale. In other words, the calculation
procedure is based solely on subjective estimates of
preferences. Another feature of the approach is that
there may be some incompatibility of estimates in
the matrix of comparative estimates of criteria.
The methodological techniques and calculation
procedures proposed below combine the
advantages of the above approaches to solving the
problem and allow (a) to significantly level
subjectivity in the evaluation of choice options and
(b) are applicable when choosing the most
problematic alternatives that require studying and
finding ways to improve their “condition”. As well
as the considered first method of choosing the best
option, the methodology is based on the
"normalization" of the distances between the actual
(observed) values of the criteria and their critical
(reference) values. However, further calculations
are carried out taking into account the weights of
each of the criteria. The weights of the criteria are
determined using the following calculation
procedure:
(1) a matrix of numbers is formed, representing
pair-wise comparative estimates of the criteria. The
comparison is carried out on a scale from 1 to 9
(you can take another interval, say, from 1 to 100:
the essence of the method will remain unchanged).
These numbers indicate a quantitative assessment
of how much one criterion is more important than
another for a given expert or a decision-maker.
Let's denote these numbers by , where and
are the numbers of the criteria being compared. In
this case, means that the criteria and are
equally important; means the absolute
superiority of criterion over criterion . The
interpretation of the values of is given in Table
1. If it turns out that criterion is less important
than criterion then the inverse value of the
corresponding index from Table 1 should be used
to numerically reflect the ratio. For example, if
criterion is noticeably less important than
criterion , then
. The score of the ratio
of criteria and is equal to
, that is
=
. (2)
The interpretation of the values of in the
matrix of pair-wise comparisons is as follows:
means that criteria and are equally
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2022.19.96