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basis of the method, there is the matrix
R
= ||r
ij
|| compiled from the defining indicators of
compared objects and statistical data (or expert assessment), and weights of the indicators
ω
i
; (
i
= 1, 2,...,
m
;
j
= 1, 2, ...,
n
, here
m
is the number of indicators and
n
is the number of
compared objects, i.e. alternatives).
Quantitative multiple criteria evaluation methods determine whether an indicator is
maximising or minimising. The best values of maximising indicators are the highest, while
the best values of minimising indicators are the lowest. The criteria in quantitative multiple
criteria methods often combine normalised values and weights of indicators. The logics
employed in the PROMETHEE method differs from other quantitative multiple criteria
methods. The decision-maker is an active participant in the phase of problem shaping and
problem solving. The decision-maker adds the priorities in the method's assessment
procedure: determines the permissible extremes of differences
q
and
s
(highest and lowest)
for each indicator (criterion)
R
i
. In the PROMETHEE method, alternatives
A
j
and
A
k
are
considered indifferent with respect to the indicator
R
i
, if the difference d
i
(
A
j
,A
k
) =
r
ij
−
r
ik
between the indicator's values r
ij
and r
ik
is below the lowest extreme value
q
. Also, the
alternative
A
j
is preferred over the alternative
A
k
if the difference is above the highest
extreme value
s
. Moreover, Decision maker sets a specific priority function
p(d)
(with the
parameters
q
and
s
) for each indicator. The function's values vary between 0 and 1, and
show the extent to which the alternative
A
j
is more important than the alternative
A
k
(with
respect to the indicator
R
i
). In practical applications, six variants of typical priority functions
p(d)
suffice (Podvezko & Podvezko, 2009). The PROMETHEE method bases its final
evaluation on all positive priorities of each alternative. The PROMETHEE I method defines
the relation of priority and indifference for all alternatives
A
j
and
A
k
with either plus or
minus:
P
+
,
P
−
,
I
+
,
I
−
. The PROMETHEE II method ranks the alternatives by the differences
F
j
= F
+
j
− F
−
j
. The PROMETHEE I method determines the best of compared alternatives (Brans
& Mareschal, 2005).
COmplex Proportional ASsessment method
(
COPRAS
). This method was developed by K.
Zavadskas, F. and A. Kaklauskas (1994), scientists from Vilnius Gediminas Technical
University. In multiple criteria analysis, it is expedient to combine the quantitative and
qualitative assessment. It is the COPRAS method that helps to analyse more aspects of one
object by combining quantitative and qualitative criteria. This method has a huge
advantage—it helps not only to compare any alternatives but also to measure their market
value. In this method, the selected alternatives are subjected to integrated analysis,
considering quantitative (e.g., operational territory, number of objects, cost of products or
services, production capacity, the replacement cost) and qualitative (e.g., restrictions
imposed by legislation and regulations, technological novelty, compliance with
environmental requirements, level of innovation, stakeholder influence, etc.) criteria of the
market conjuncture, which describe the object.
It is easy to express quantitative criteria by the quantitative measures of your choice
(amount of money, technical parameters, etc.), but in case of qualitative criteria expressed by
conditional measures (scores, percentages) it is a more complex procedure to measure their
values and weights. Weights for qualitative criteria must be identified through analysis,
scientific studies and databases, by comparing equivalents, and by analysing macro-, meso-
and microenvironment in regions with similar development degrees or development trends.
Comparability demands for normalisation of the values of quantitative and qualitative
criteria using relevant formulas. The expert assessment method is the most popular when it
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