Improved OCRA Method Based on the Use of Interval Grey Numbers

Abstract

Multiple Criteria Decision Making (MCDM) denotes the selection of the alternatives based on a set of, often conflicting, criteria. As a result of using it for solving a large number of decision-making problems, a number of MCDM methods have been proposed. Some of these methods are further adapted to use grey numbers, with the aim of ensuring their broader usage. The Operational Competitiveness Rating (OCRA) method is a less frequently used MCDM method, for which the grey extension has not been proposed yet. Therefore, an improved OCRA method is proposed in this paper. In the proposed approach, the ordinary OCRA method is adapted for the purpose of enabling the use of grey numbers, which has enabled its usage for solving decision-making problems associated with uncertain and partially known information. In addition to this, in the improved OCRA method the original normalization procedure has been replaced by a new one. Finally, the usability and effectiveness of the proposed approach are checked on two numerical illustrations. The first is taken from the literature. The ranking results obtained by using the improved OCRA method are the same as the results obtained by using two prominent MCDM methods, which confirms the usability of the proposed approach. In the second one, the usability and efficiency of the improved OCRA method are verified in the case of the selection of the best capital investment project.

Full text

Available online at www.researchinformation.co.uk
The Journal of Grey System
Volume 29 No.4, 2017
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Improved OCRA Method Based on the Use of
Interval Grey Numbers
Dragisa Stanujkic
1
, Edmundas Kazimieras Zavadskas
2
, Sifeng Liu
3,4
,
Darjan Karabasevic
5
, Gabrijela Popovic
1
1. Faculty of Management in Zajecar, John Naisbitt University, Park Suma
Kraljevica bb, Zajecar 19000, Serbia.
2. Research Institute of Smart Building Technologies, Civil Engineering Faculty
Vilnius Gediminas Technical University, Saulėtekio al. 11, Vilnius 10221, Lithuania.
3. College of Economics and Management, Nanjing University of Aeronautics and
Astronautics, Nanjing 211106, P.R. China.
4. Institute for Grey Systems Studies, Nanjing University of Aeronautics and
Astronautics, Nanjing 211106, P.R. China.
5. Faculty of Applied Management, Economics and Finance, University Business
Academy in Novi Sad, Jevrejska 24, Belgrade 11000, Serbia
Abstract
Multiple Criteria Decision Making (MCDM) denotes the selection of the
alternatives based on a set of, often conflicting, criteria. As a result of using it for
solving a large number of decision-making problems, a number of MCDM methods
have been proposed. Some of these methods are further adapted to use grey
numbers, with the aim of ensuring their broader usage. The Operational
Competitiveness Rating (OCRA) method is a less frequently used MCDM method,
for which the grey extension has not been proposed yet. Therefore, an improved
OCRA method is proposed in this paper. In the proposed approach, the ordinary
OCRA method is adapted for the purpose of enabling the use of grey numbers,
which has enabled its usage for solving decision-making problems associated with
uncertain and partially known information. In addition to this, in the improved
OCRA method the original normalization procedure has been replaced by a new
one. Finally, the usability and effectiveness of the proposed approach are checked
on two numerical illustrations. The first is taken from the literature. The ranking
results obtained by using the improved OCRA method are the same as the results
obtained by using two prominent MCDM methods, which confirms the usability of
the proposed approach. In the second one, the usability and efficiency of the
improved OCRA method are verified in the case of the selection of the best capital
investment project.
Keywords: Multiple Criteria Decision Making; MCDM; OCRA; Improved
OCRA; Interval Grey Numbers

Corresponding Author: Dragisa STANUJKIC, Faculty of Management in Zajecar, John Naisbitt
University, Park Suma Kraljevica b.b., Zajecar 19000, Serbia; Email:
dragisa.stanujkic@fmz.edu.rs
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1. Introduction
Multiple Criteria Decision Making (MCDM) denotes the selection and/or
ranking of the alternatives based on a set of, often conflicting, criteria. As the results
of the significant number of the studies conducted in this field, a number of
prominent MCDM methods have been proposed, such as: Simple Additive
Weighting (SAW)
[1,2]
, Technique for Order of Preference by Similarity to Ideal
Solution (TOPSIS)
[3]
, Preference Ranking Organization Method for Enrichment
Evaluations (PROMETHEE)
[4]
, the ELimination and Choice Expressing Reality
(ELECTRE)
[5]
family and Multi-criteria Optimization and Compromise Solution
(VIKOR)
[6]
.
Beside the above-mentioned, there are a number of significantly less frequently
used MCDM methods, such as: Organization, Rangement Et Synthese De Donnes
Relationnelles (ORESTE)
[7]
, Operational Competitiveness Rating (OCRA)
[8]
,
Closed Procedures near Reference Situations (ZAPROS)
[9]
, Interactive and
Multi-criteria Decision Making (TODIM)
[10,11]
, Kemeny Median Indicator Rank
Accordance (KEMIRA)
[12]
, Evaluation Based on Distance from Average Solution
(EDAS)
[13]
and so on.
Although OCRA can be classified as a rarely used MCDM method, it was
successfully used for solving various decision-making problems in various areas,
such as: performance and efficiency measurement
[14]-[22]
, manufacturing
[23,24,25,26]
,
the location selection
[27]
, the material selection
[28,29]
, the hotel selection
[30]
and so on.
The above, so-called classical, MCDM methods are mainly based on the use of crisp
numbers. However, a significant number of real decision-making problems are
accompanied by some kinds of predictions and uncertainties, for which reason the
classical MCDM methods are not suitable for solving them.
Significant progress in terms of solving such problems was provided after
Zadeh
[31]
and Deng
[32]
had proposed the fuzzy set theory and the grey set theory,
respectively. Based on the fuzzy and the grey set theories, many ordinary MCDM
methods have further been extended with the aim of applying fuzzy or grey numbers,
i.e. their usage is ensured for solving a much larger number of real decision-making
problems.
The Grey System Theory is identified in many studies as an effective
methodology that can be used to solve decision-making problems with partially
known information. Therefore, many ordinary MCDM methods are extended for the
purpose of using interval grey numbers.
The following extensions can be mentioned as some of these: Grey
TOPSIS
[33,34,35]
, COPRAS-G
[36]
, SAW-G
[37,35]
, ARAS-G
[38]
, the grey extension of the
LINMAP
[39]
method, the grey extension of the MOORA
[40,41]
method, Grey AHP
[42]
,
Grey Compromise Programming
[43]
and so on.
The above-mentioned grey extensions are successfully used for solving a large
number of different problems, such as: the supplier selection
[44,45]
, air traffic
management
[46]
, the supply chain performance benchmarking
[47]
, the selection of the
inside thermal insulation
[48]
, the assessment of the structural systems of high-rise
buildings
[49]
, the social media platform selection
[50]
, the market segment
evaluation
[51]
, the building foundation alternatives selection
[52]
, the robot selection
[53]
and so on.
In order to enable the use of the OCRA methods for solving a much larger
number of decision-making problems, i.e. problems placed in imprecise and
uncertain environments, the grey extension of the OCRA method is proposed in this
paper.
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
Therefore, the remaining part of the paper is organized as follows: In Section 2,
some basic elements of the Grey System Theory are presented. In Section 3, the
OCRA method is demonstrated. In Section 4, an extension of the OCRA method
adapted for the purpose of using interval grey numbers is discussed. In section 5,
numerical illustrations are considered in order to verify the proposed approach.
Finally, Section 6 presents the conclusions.
2. Grey Numbers and Their Operations
In the Grey System Theory, several types of grey numbers are proposed, of
which black, white and interval grey numbers are emphasized here.
Definition 1 A grey number, denoted as x

, is such a number whose exact
value is unknown, but the range within which the value lies is known. A grey number
with the known upper, x, and the lower,
x
, bounds, but the unknown distribution
information for x is called the interval grey number
[54,55]
:
]|[],[ xxxxxxxx 
¢

¢
=
. (1)
Definition 2 The distance between the bounds of an interval grey number
xxxl -= )(
is called the length of the information field of the grey number x

, or
more shortly, the length of the grey number. When the length of an interval grey
number increases and the bounds tend to infinity,
-®x
and
+®
x, then the
interval grey number tends to become a black number. In contrast to the previous one,
when the length decreases, then the interval grey number tends to become a white
number; finally, when the upper and the lower bounds are equal,
xx =
, such an
interval grey number becomes a white (crisp) number
[56]
.
Definition 3
The basic operations of interval grey numbers. Let
] ,[
1
1
1
xxx  , and ] ,[
2
2
2
xxx  be the two interval grey numbers. The basic
operations of the interval grey numbers
1
x
and
2
x
are defined as follows
[55,57]
:
] ,[
21
21
21
xxxxxx +++ ,
(2)
] ,[
2
12
1
21
xxxxxx --- , (3)
}],,,max{ },,,,min{[
21
2
12
121
21
2
12
121
21
xxxxxxxxxxxxxxxxxx ´
, (4)
] ,, ,max , ,, ,min[
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
21

þ

ý
ü

î

í
ì

þ

ý
ü

î

í
ì
 x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
xx , (5)
],[
1
1
1
xkxkxk  . (6)
Here, k is a positive real number and for Eq. (5)
0
2
x
and
0
2
x
.
Definition 4 The whitened value. The whitened value of an interval grey
number
)(

x
is a crisp number whose possible values lie between the upper and the
lower bounds of the interval grey number x

. For the given interval grey number
],[ xxx 
, the whitened value
)(

x
can be determined as follows
[55,57]
:
xxx


+-=
)1(
)(
, (7)
where

denotes the whitening coefficient and
]1,0[


. In the particular case,
when 5.0
=

, the whitened value becomes the mean of the interval grey number, as
follows:
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OCRA
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
)(
2
1
)5.0(
xxx +=
=

. (8)
3. Operational Competitiveness Rating Method
As previously mentioned, the OCRA method was proposed by Parkan
[8]
and
further developed by Parkan and Wu
[58,59,60]
.
This method was initially developed in order to measure the relative
performances of a set of production units, where resources are consumed to create
value-added outputs
[28]
. Later, this method was used to solve other various multiple
criteria decision-making problems.
Parkan
and Wu
[58]
state that this method applies an intuitive approach to
incorporating the decision maker’s preferences for the relative importance of the
criteria. According to Chatterjee and Chakraborty
[28]
, the main advantage of the
OCRA method is that it can deal with those MCDM situations in which the relative
weights of the criteria are dependent on the alternatives and different weight
distributions are assigned to the criteria for different alternatives, whereas some of
the criteria are not applicable to all the alternatives, either.
The main idea of the OCRA method is to perform the independent evaluation of
alternatives with respect to benefit and cost criteria, and finally to combine these two
aggregate ratings so as to obtain competitiveness ratings, which helps decision
makers not to lose information during the decision-making process
[61]
.
Based on Parkan and Wu
[60]
, Chatterjee and Chakraborty
[28]
and Liu et al.
[62]
,
the computational procedure of the improved OCRA method can be described
through the following steps:
Step 1 Calculate the aggregate performance ratings for the cost criteria, as
follows:
]1,1[
min
max
min
-
-
å
=
 ijj
ijijj
jji
x
xx
wI
, (9)
where
i
I denotes the aggregate performance rating of the alternative i,
obtained on the basis of the cost (Input) criteria, x
ij
denotes the performance rating
of the alternative i with respect to the criterion j and
min

is the set of the cost
(minimization) criteria.
Based on Liu et al.
[62]
Eq. (9) could be replaced with the following one:
]1,1[
minmax
max
min
-
-
-
å
=
 ijjijj
ijijj
jji
xx
xx
wI
. (10)
Step 2 Calculate the linear performance ratings for the cost criteria, as follows:
i
i
ii
III min-= , (11)
where
i
I
denotes the linear performance rating of the alternative i, obtained
on the basis of the cost criteria.
The linear scaling in the OCRA method is made with the aim of assigning zero
ratings to the least preferable alternative.
Step 3 Calculate the aggregate performance ratings with respect to the benefit
criteria, as follows:
]1 ,1[
min
min
max
-
-
å
=
 ijj
ijjij
jji
x
xx
wO
, (12)
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OCRA
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
where
i
O denotes the aggregate performance rating of the alternative i,
obtained on the basis of the benefit (Output) criteria, and
max

denotes the set of
the benefit (maximization) criteria.
Based on Liu et al.
[62]
Eq. (11) could be replaced with the following equation:
]1 ,1[
minmax
min
max
-
-
-
å
=
 ijjijj
ijjij
jji
xx
xx
wO
. (13)
Step 4 Calculate the linear performance ratings for the benefit criteria, as
follows:
i
ii
i
OOO min-= , (14)
where
i
O
denotes the linear performance rating of the alternative i, obtained
on the basis of the benefit criteria.
Step 5 Calculate the overall performance ratings, as follows:
)min(
i
i
i
i
i
OIOIP +-+= , (15)
where
i
P
denotes the overall performance rating of the alternative i.
Step 6 Select the most appropriate alternative. Based on the OCRA method, the
alternative with the highest value of P
i
is the most appropriate.
The computational procedure of the OCRA method is based on the use of the
distance to the least preferable performances of the criteria, i.e.
ijijj
xx
-
max
for
the cost criteria, and
ijjij
xx min
-
for the benefit criteria. That indicates a certain
similarity to the prominent TOPSIS and VIKOR methods.
However, the OCRA method has its particularities; the specific normalization
procedure shown in Eqs (9) and (11) can be mentioned as one the most significant.
Contrary to commonly used normalization procedures, the normalization procedure
used in the ordinary OCRA method does not enable the values of normalized
performance ratings to always belong to [0,1], whereas in particular cases these
values can be greater than that one.
An improvement of the OCRA method is made by replacing Eqs (9) and (12)
with Eqs (10) and (13), thus enabling the normalized performance ratings to always
belong to [0,1].
Due to the particularities of the OCRA method, the comparison of the results
obtained by using TOPSIS, VIKOR, SAW and OCRA is shown in Appendix A.
4. Improved Operational Competitiveness Rating Method
In order to enable the usage of the OCRA method for solving MCDM problems
accompanied by predictions and uncertainties, an extension of the OCRA method,
adapted for the usage of interval grey numbers, is proposed in this section.
The computational procedure of the proposed grey extension of the OCRA method
can be shown as follows:
Step 1 Calculate the grey aggregate performance ratings for the cost criteria, as
follows:
ijjijj
ijijj
jji
xx
xx
wI -
-
å
=

minmax
max
min
, (16)
where
i
Idenotes the grey aggregate performance rating of the alternative i,
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OCRA
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
obtained on the basis of the cost criteria,
],[
ijijij
xxx
¢¢¢

denotes the grey
performance rating of the alternative i with respect to the criterion j,
]max,[maxmax
ijjijjijj
xxx
¢¢¢

and
]min,[minmin
ijjijjijj
xxx
¢¢¢

.
On the basis of the operations of interval grey numbers, Eq. (16) can also be
shown as follows:
]min,[min]max,[max
],[]max,[max
min
ijjijjijjijj
ijijijjijj
jji
xxxx
xxxx
wI ¢¢¢
-
¢¢¢
¢¢¢
-
¢¢¢
å
=

, (16a)
or as:
]minmax,min[max
]max,[max
min
ijjijjjijj
ijijjijijj
jji
xxxx
xxxx
wI ¢
-
¢¢¢¢
-
¢
¢
-
¢¢¢¢
-
¢
å
=

. (16b)
Step 2 Calculate the grey linear performance ratings for the cost criteria, as
follows:
i
i
ii
III -= min , (17)
where ],[
iii
III ¢¢¢
 denotes the grey linear performance ratings of the
alternative i, obtained on the basis of the cost criteria, and
]min,[minmin
i
i
i
i
i
i
III ¢¢¢

.
Eq. (17) can also be written as follows:
]min,min[
i
i
ii
i
ii
IIIII ¢
-
¢¢¢¢
-
¢
 . (17a)
Step 3 Calculate the grey aggregate performance ratings for the benefit criteria
in the following manner:
ijjijj
ijjij
jji
xx
xx
wO -
-
å
=

minmax
min
max
, (18)
where
],[
iii
OOO ¢¢¢

denotes the grey aggregate performance rating of the
alternative i.
Eq. (18) can also be shown as follows:
]min,[min]max,[max
]min,[min],[
max
ijjijjijjijj
ijjijjijij
jj
i
xxxx
xxxx
wO ¢¢¢
-
¢¢¢
¢¢¢
-
¢¢¢
å
=

, (18a)
or as:
]minmax,min[max
]min,min[
max
ijjijjjijj
ijjijjij
jj
i
xxxx
xxxx
wO ¢
-
¢¢¢¢
-
¢
¢
-
¢¢¢¢
-
¢
å
=

. (18b)
Step 4 Calculate the linear performance ratings for the benefit criteria, as
follows:
i
ii
i
OOO -= min , (19)
where ],[
iii
OOO ¢¢¢
 denotes the grey linear performance ratings of the
alternative i, obtained on the basis of the benefit criteria, and
]min,[minmin
i
i
i
i
i
i
OOO ¢¢¢

.
Eq. (19) can also be shown as follows:
]min,min[
i
i
ii
ii
i
OOOOO ¢
-
¢¢¢¢
-
¢
 . (19a)
Step 5 Calculate the overall grey performance ratings. The overall performance
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
rating for each alternative could be calculated as follows:
)min(
i
i
i
i
i
OIOIP +-+= . (20)
Eq. (20) can also be shown as follows:
)](min),(min[
i
i
i
i
i
i
i
i
i
i
i
OIOIOIOIP ¢
+
¢
-
¢¢
+
¢¢¢¢
+
¢¢
-
¢
+
¢
 . (20a)
Step 6. Select the most appropriate alternative. Based on the use of the improved
OCRA method, the overall grey performance ratings
i
P
should be transformed
into the overall crisp performance ratings
i
P
before the ranking, which can be done
by applying Eq. (7).
In this way, the decision makers involved in the evaluation can consider
scenarios ranging from pessimistic to optimistic by varying the values of the
coefficient

.
5. Numerical Illustrations
In this section, two numerical illustrations are considered in order to explain the
proposed methodology in detail and confirm its usability. The first was taken from
the literature, whereas the second was particularly prepared for the purpose of this
manuscript.
5.1. The First Numerical Illustration
In the sub-second numerical illustration, adopted from Zavadskas et al.
[37]
, the
selection of the contractors for the construction of prefabricated wooden
shield-shaped houses is considered. The selected criteria, the criteria weights and the
performance ratings are shown in Table 1.
Table 1 The initial grey decision-making matrix
Criteria
Experience of
executives
Number of
constructed houses
Turnover Number of
executives
Market share
Production
method
years units 10
6
€ persons portion of sales
points
max max max min max max
w
i
0.22 0.26 0.11 0.09 0.15 0.17
C
1
C
2
C
3
C
4
C
5
C
5
x’ x

x’ x

x’ x

x’
x

x’ x

x’ x

A
1
11 15
10 15 3.30
4.50
35
48 0.152
0.203
1 2
A
2
10 14
7 13 2.54
3.68
40
58 0.111
0.162
1 2
A
3
14 18
5 9 1.95
2.46
42
53 0.079
0.121
1 3
A
4
12 16
1 4 0.42
1.73
15
63 0.010
0.054
1 2
A
5
6 10
2 9 0.62
2.67
10
46 0.120
0.122
1 2
The computational data obtained by using the improved OCRA method are shown in
Table 2.
Table 2 The computational data obtained by using improved OCRA
i
I
i
I
i
O
i
O
i
P
Alternatives x’ x

x’ x

x’ x

x’ x

x’ x

A
1
-0.63
0.14
0.08
1.85
-0.72
1.33 -0.93
2.36
-4.50
6.48
A
2
-0.52
0.36
-0.05
1.59
-0.61
1.55 -1.06
2.09
-4.52
6.44
A
3
-0.47
0.25
-0.22
1.49
-0.56
1.44 -1.23
1.99
-4.65
6.23
A
4
-1.08
0.47
-0.42
1.01
-1.17
1.67 -1.43
1.51
-5.45
5.97
A
5
-1.19
0.09
-0.50
1.07
-1.28
1.28 -1.51
1.57
-5.65
5.65
The grey aggregate and grey linear performance ratings for the cost criteria are
calculated by using Eqs (16) and (17), whereas the grey aggregate and grey linear
Improved
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Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
performance ratings for the cost criteria are calculated by using Eqs (18) and (19).
Finally, the overall grey performance ratings are calculated by using Eq. (20).
The ranking order of the considered alternatives, obtained by using Eq. (7) and

=
0.5, are shown in Table 3.
Table 3 The ranking orders of the considered alternatives
Alternatives P
i
Rank
A
1
0.99 1
A
2
0.96 2
A
3
0.79 3
A
4
0.26 4
A
5
0.00 5
Finally, in Table 4, the comparison of the ranking results obtained by the
improved OCRA method and the results obtained in Zavadskas et al.
[37]
are shown.
Table 4 The comparison of the ranking orders obtained by using COPRAS-G and improved OCRA
Alternatives
Zavadskas et al.
[37]
Improved OCRA
SAW-G TOPSIS-G
Rank Rank Rank
A
1
1 1 1
A
2
2 2 2
A
3
3 3 3
A
4
5 5 4
A
5
4 4 5
According to the comparison shown in Table 4, the ranking orders of the
considered alternatives obtained by the proposed improvement of the OCRA method
are similar to the ranking orders obtained in Zavadskas et al.
[37]
, which confirms the
usability of the proposed improvement of the OCRA method.
It is not easy to say that a certain MCDM method is dominant in relation to
another because each one of them has its own computation and ranking logic, as well
as certain specificities. The improved OCRA method enables the usage of grey
numbers, for which reason it can be used for solving a larger number of complex
decision-making problems, while its computational and ranking procedures remain
understandable and relatively easy to use.
5. 2 The Second Numerical Illustration
In this numerical illustration, the improved OCRA method is used in order to
choose the best capital investment project, or more precisely, to enable the selection
of investment in the most appropriate type of hotels in a ski center. The usage of the
Grey OCRA method has been considered in the case of the ski center Besna Kobila,
an almost unknown ski center in southeastern Serbia, near the frontier of Serbia,
Bulgaria and FYRoM (Macedonia), which could be very attractive in the future. Five
types of hotels have been evaluated on the basis of the following four criteria:
- Number of units (C
1
),
- Surface of accommodation units (C
2
),
- Capital investments costs (C
3
), and
- Annual operating income per accommodation unit (C
4
).
The available alternatives and their ratings, adopted from the business plan for
the tourism destination Besna Kobila, are accounted for in Table 5. The weights of
the criteria, obtained on the basis of the three experts’ opinions by using the
SWARA
[63]
method, are also given in Table 5.
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56

Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
Table 5 Estimated ratings for accommodation units at the Ski Center Besna Kobila
C
1
C
2
C
3
C
4
Alternatives m
2
€/m
2
€
Optimization
max max min max
Destination hotel A
1
100 30-80 900-950 25000-30000
Apartments A
2
100 60-90 800-850 15000-20000
Condotel A
3
100 40-80 800-900 15000-20000
Townhouse A
4
25 70-90 850-950 10000-20000
Chalet A
5
10 100-130 900-1000 20000-35000
Source: Available at: http://mtt.gov.rs/download/sektor-za-turizam/master-planovi/
master_plan_besna_kobila_finalno.pdf (In Serbian, accessed the last time: 16
th
Dec. 2016).
The computational details obtained by using the improved OCRA method based
on the use of interval grey numbers, as well as the overall performances and the
ranking order of the evaluated alternatives, are demonstrated in Tables 6 and 7.
Table 6 The computational details obtained by using Improved OCRA
Alternatives
i
I
i
I
i
O
i
O
i
P
x’ x

x’ x

x’ x

x’ x

x’ x

A
1
-0.32
-0.32
0.32
0.32
-0.12
-0.12
0.51
0.51
0.51
0.51
A
2
0.08 0.08 0.71
0.71
-0.22
-0.22
0.41
0.41
0.81
0.81
A
3
0.00 0.00 0.63
0.63
-0.39
-0.39
0.24
0.24
0.56
0.56
A
4
-0.32
-0.32
0.32
0.32
-0.63
-0.63
0.00
0.00
0.00
0.00
A
5
-0.63
-0.63
0.00
0.00
0.03
0.03 0.67
0.67
0.35
0.35
Table 7 The ranking orders of the considered alternatives
Alternatives P
i
Rank
A
1
0.51 3
A
2
0.81 1
A
3
0.56 2
A
4
0.00 5
A
5
0.35 4
As can be seen from Table 7, the best investment alternative for the Ski Center
Besna Kobila is investment in Apartments.
6. Conclusion
This paper presents an improvement of the OCRA method based on the use of
interval grey numbers.
On the basis of the proposed improvement, the OCRA method can be used more
efficiently for solving a larger number of complex real-world decision-making
problems, especially those associated with uncertainty and partially known
information; so, it can be applied in many fields for the purpose of analysis,
modelling and forecasting.
Finally, the usability and effectiveness of the proposed approach are checked on
the two numerical illustrations. The first was taken from the literature. The ranking
results obtained by using the improved OCRA method are the same as the results
obtained by using the two prominent MCDM methods, which confirms the usability
of the proposed approach. In the second, the usability and efficiency of the improved
OCRA method are verified in the case of the selection of the best capital investment
project.
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57

Dragisa Stanujkic et al/ The Journal of Grey System 2017 (29)
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