Upgrading the old vernacular building to contemporary norms: multiple criteria approach.
Siozinyte, Egle ; Antucheviciene, Jurgita ; Kutut, Vladislavas 等
Introduction
Sustainable building development includes such principles as
creating healthy environment, using green materials and technologies,
energy and other natural resource savings, recycling, reusing, etc.
Sustainable building development is topical today and is taken into
consideration by various researchers. They analyse problems related with
energy efficiency and building's envelope (Ourghi et al. 2007;
Parasonis et al. 2012; Yiiksek, Esin 2013; Kazanasmaz et al. 2014);
building materials (Binici et al. 2014; Pajchrowski et al. 2014);
analyse importance of buildings' modernisation (Staniunas et al.
2013; Volvaciovas et al. 2013a); create strategies related with building
upgrading (Volvaciovas et al. 2013b; Itani et al. 2013).
There are lots of buildings that require a new approach to their
complexion. Old vernacular buildings also require a new approach. These
buildings often do not satisfy some important parameters of sustainable
development, e.g. daylighting and/or thermal performance (energy saving
aspect). Buildings use a lot of energy for their lighting and/or
heating. Modernization of these buildings can help to reduce energy
consumption. But in this case we face the problem that commonly used
modernization solutions are hardly compatible with preservation of
traditional vernacular buildings' appearance.
Some parts of the building, such as walls and windows, are the most
affected and can make a huge influence on building's appearance
while seeking to satisfy contemporary building norms. Thermal insulation
could be added to the walls; windows could be resized, the quantity of
windows or their style could be changed. Other parts of the building,
such as roof, floor, doors, base, etc. can be changed/modernised/renewed
quite easily and do not make significant influence from the visual
aspect.
The current research is the continuous work about balance between
contemporary norms and tradition continuity. Earlier research described
the possible indoor daylighting problem and presented possible ways of
improving indoor daylighting for vernacular architecture when trying to
save tradition and satisfy minimal daylighting norms determined in the
building regulations. The problem was analysed using Multiple Criteria
Decision Making (MCDM) methods such as AHP, COPRAS, TOPSIS, WASPAS
(Siozinyte, Antucheviciene 2013).
[FIGURE 1 OMITTED]
The aim and the novelty of the current research is to evaluate the
whole vernacular building (not one specific part, e.g. windows, like it
was made earlier) using multiple criteria approach and grey system
theory. Some researchers applied MCDM methods for rural buildings'
development through re-using, preservation, conservation, regeneration,
etc., aspects. They are seeking for ranking the rational solutions, such
as, rural buildings' regeneration alternatives (Zavadskas,
Antucheviciene 2007); evaluating rational solutions for rural ITC
centers (telecenters) (Hashemkhani Zolfani et al. 2012); allowing the
reduction of deterioration models of rural buildings subjectively (Cano
et al. 2013); identifying the best re-use variant of an abandoned rural
village (Russo et al. 2013). Overall, MCDM methods are suitable for
various kinds of complex construction economics problems (Kaplihski,
Tupenaite 2011; Zavadskas, Turskis 2011).
Other researchers analyze vernacular architecture in different
aspects separately. Topical themes are related with building
technologies and indoor environment (Hoof, Dijken 2008; Foruzanmehr,
Vellinga 2011), external appearance (Porto, Cascone 2013), ecology,
energy efficiency (Keizikas et al. 2012), etc.
For this case study the research object is analysed from the aspect
of sustainable development and tradition continuity and using multiple
quantitative and qualitative criteria. Nine possible variants for
vernacular building modernization are proposed and ten criteria for
their evaluation are suggested. Each criterion is weighted using
Analytic Hierarchy Process. Criteria are expressed in intervals using
grey numbers. Variants of building modernisation are ranked and the most
suitable is selected using TOPSIS Grey method.
1. Searching the most suitable way of modernisation for vernacular
building
1.1. Object
The research is exemplified by the case study. Object of the case
study is the vernacular dwelling from Aukstaitija region, Lithuania
(Fig. 1). Wooden building was constructed at the end of XIX century. The
architecture is typical for the region's rural architecture: sloped
straw roof, 20 cm wide log walls, 0.7*1.0 m windows, stone foundation.
Building is situated to the North-East direction at the site.
1.2. Building modernisation alternatives and criteria for
assessment of solutions
Chosen vernacular building does not satisfy contemporary
daylighting and thermal performance norms. The aim is to find the
rational architectural solution that combines contemporary norms and
tradition continuity.
Four components, such as architectural heritage, requirements
(norms), energy and comfort are proposed for searching rational
solutions for old vernacular architecture. Each component can be
described by various criteria. According to Figure 2 the criteria system
have been formulated for the case study.
[FIGURE 2 OMITTED]
Criteria for ranking the variants of building renovation are
presented in Table 1.
Criteria are evaluated using quantitative ([x.sub.1], [x.sub.2],
[x.sub.3], [x.sub.6], [x.sub.7], [x.sub.8]) and qualitative ([x.sub.4],
[x.sub.5], [x.sub.9], [x.sub.10]) measures. Quantitative measures are
evaluated according to Technical Construction Regulations for the
buildings (STR 2.02.01:2004; STR 2.05.01:2005). Qualitative measures are
evaluated using the scale based on five-level Likert item scale (1-very
weak; 2-weak; 3-medium; 4-strong; 5-very strong).
Alternatives are formed considering the mentioned above energy
parameters through the energy saving aspect. Windows and walls are the
parts of the building that have influence on the external
building's appearance when trying to satisfy daylighting and
thermal performance norms as described in building regulations. The
original 0.20 m wooden wall has a quite good thermal resistance and it
is possible that together with solar energy inflows through the building
external envelope can reach required thermal performance. Other parts of
the building (floor, roof, doors, base, etc.) are not taken into
consideration due to their small influence to building's appearance
when upgrading the building.
Figure 3 demonstrates wall types for this case study: a) original
wall (without thermal insulation); b) thermal insulation added outside
the wall; c) thermal insulation added inside the room.
[FIGURE 3 OMITTED]
Window variants for solving daylighting problems are described in
detail by Siozinyte and Antucheviciene (2013). Also, some of criteria
are taken from a previous research.
Possible alternatives for building renovation are composed of
different wall and window modernization solutions. Analysed alternatives
for building renovation are as follows: [a.sub.1] wall without thermal
insulation and increased size of the window, while maintaining the
typical traditional proportions; [a.sub.2]--wall without thermal
insulation and increased quantity of the windows; [a.sub.3]--wall
without thermal insulation and used the new glass structures for
building facades (modern window solution); [a.sub.4]--thermal insulation
added outside the wall and the window size increased, while maintaining
the typical traditional proportions; [a.sub.5]--thermal insulation added
outside the wall and increased quantity of the windows;
[a.sub.6]--thermal insulation added outside the wall and used the new
glass structures for building facades (modern window solution);
[a.sub.7]--thermal insulation added inside the room and the window size
increased, while maintaining the typical traditional proportions;
[a.sub.8]--thermal insulation added inside the room and increased
quantity of the windows; [a.sub.9]--thermal insulation added inside the
room and used the new glass structures for building facades (modern
window solution).
2. Methodology for ranking of alternatives
2.1. AHP method
AHP method is based on pairwise comparisons of criteria. This
method was introduced by Saaty (1980) for measuring the intensity of
importance of criteria according to the experts' opinion.
For this case study the expert team from 6 civil engineers and 10
architectural engineers (16 experts at all) was created. Experts'
judgment on importance of criteria was expressed using the scale from 1
to 5 in the current case. The decision about the consistency of
performed comparisons was made on the basis of the Consistency Ratio
(CR). Geometric mean technique was used to aggregate judgments of all
experts.
2.2. TOPSIS Grey method
TOPSIS method with grey numbers was introduced by Lin et al.
(2008). The method is used for problem solving with uncertain
information and presented with reference to Zavadskas et al. (2010),
Hashemkhani Zolfani et al. (2012), also Hashemkhani Zolfani and
Antucheviciene (2012).
TOPSIS Grey method includes the following steps:
1. Describing alternatives and selecting important criteria.
2. Constructing the decision-making matrix [cross product] X :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
where: [cross product] [x.sub.ij] enotes the grey evaluations of
the ith alternative with respect to the jth attribute [[cross product]
[x.sub.i1] [cross product] [x.sub.i2] ... [cross product] [x.sub.im];
the grey number evaluation series of the ith alternative.
3. Constructing the normalised decision-making matrix. Normalised
values of maximizing and minimizing attributes are calculated as
follows:
[cross product] [[bar.x].sub.ij,b] = [cross product]
[x.sub.ij]/[max.sub.i]([b.sub.ij]) =
([w.sub.ij]/[max.sub.i]([b.sub.ij]); [b.sub.ij]/[max.sub.i]([b.sub.ij]))
(2)
and
[cross product] [[bar.x].sub.ij,w] = [cross product]
[x.sub.ij]/[max.sub.i]([b.sub.ij]) = (1 -
[b.sub.ij]/[max.sub.i]([b.sub.ij]); [w.sub.ij]/[max.sub.i]([b.sub.ij])).
(3)
4. Weighting the normalised decision-making matrix.
5. Determining ideal and negative-ideal solutions. The positive
ideal alternative [A.sup.+], and the negative ideal alternative
[A.sup.-] can be defined as follows:
[A.sup.+] = {([max.sub.i][[bar.b].sub.ij]|j [member of] J),
([min.sub.i][[bar.w].sub.ih]|j [member of] J'), i [member of] n} =
{[[bar.x].sup.+.sub.1], [[bar.x].sup.+.sub.2],...,
[[bar.x].sup.+.sub.m]} (4)
and
[A.sup.-] = {([min.sub.i][[bar.w].sub.ij]|j [member of] J),
([max.sub.i][[bar.b].sub.ih]|j [member of] J'), i [member of] n} =
{[[bar.x].sup.-.sub.1], [[bar.x].sup.-.sub.2], ...,
[[bar.x].sup.-.sub.m]} (5)
6. Calculating the separation measure from the positive and
negative ideal alternatives:
[L.sup.+.sub.i] = [square root of [1/2] [m.summation over (j = 1)]
[q.sub.i] [[absolute value of [[bar.x].sup.-.sub.j] -
[[bar.b].sub.ij]].sup.2] + [[absolute value of [[bar.x].sup.-.sub.j] -
[[bar.b].sub.ij]].sup.2]] (6)
and
[L.sup.-.sub.i] = [square root of 1/2 [m.summation over (j = 1)]
[q.sub.i] [[absolute value of [[bar.x].sup.+.sub.j] -
[[bar.b].sub.ij]].sup.2] + [[absolute value of [[bar.x].sup.+.sub.j] -
[[bar.b].sub.ij]].sup.2]] (7)
7. Calculating the relative closeness K+ to the positive ideal
alternative for the group:
[K.sup.+.sub.i] = [L.sup.-.sub.i]/[L.sup.+.sub.i] +
[L.sup.-.sub.i], 0 [less than or equal to] [K.sup.+.sub.i] [less than or
equal to] 1. (8)
8. Ranking the preference order.
TOPSIS Grey method was chosen by its suitability for problem
solving with uncertain information, expressed in intervals. For this
case study information related with thermal insulation materials is
considered to be uncertain information. It is not very important to
choose the exact thermal insulation material at the first stage of the
research. At the first stage the type of materials can be chosen, i.e.
from raw materials (straws, sheep wool, etc.) to various kinds of
mineral wools. The particular thermal insulation material could be
chosen in the next step of the research, after selecting the alternative
of buil ding modernisation/renovation and the type of thermal insulation
material simultaneously.
3. Calculation results: weighting criteria and evaluating the
alternatives
Weights of the criteria [w.sub.i] are determined by applying AHP
method (Table 2).
The Consistency Ratio coefficient is calculated as follows (for
description of methodology see Saaty 1980; Wang et al. 2013; Siozinyte,
Antucheviciene 2013):
1) [[lambda].sub.max] = 10.1220; 2) CI = 0.0135; 3) RCI = 1.4900;
4) CR = 0.0091.
The Consistency Ratio does not exceed the condition CR < 0.1. It
means that the judgements are consistent and the weights of criteria can
be used for the further alternative ranking.
The alternatives ranking when applying TOPSIS Grey method is
presented in Tables 3-6.
According to the results (Table 6) the alternatives are ranked as
follows:
[a.sub.7] > [a.sub.8] > [a.sub.9] > [a.sub.4] >
[a.sub.5] > [a.sub.6] > [a.sub.1] > [a.sub.2] > [a.sub.3].
In the case study the best alternative is the alternative [a.sub.7]
where thermal insulation is added to the wall inside the room and the
window size increased, while maintaining the typical traditional
proportions when seeking to improve daylighting and thermal performance
parameters and to meet current building regulations/norms.
By the ranking of weights of the criteria it is seen that thermal
performance properties are more important than daylighting properties
for this case study's experts. When talking about the external
appearance of the building, the results show that priority is taken to
architecture with traditional appearance (traditional type of the window
and traditional view of the wall), no matter that the building does not
meet daylighting norms.
Dividing experts into the groups by their professions, the results
showed that civil engineers and architectural engineers evaluate
alternatives quite similarly: the three best alternatives are [a.sub.7]
> [a.sub.8] > [a.sub.9] (the same as the both groups evaluated
together). The further alternatives are ranked differently and it is
seen that architectural engineers give their priority to the
architectural properties and civil engineers give their priority to the
energy saving parameters. Also it can be noticed that both groups
understand the importance of saving traditional building's
appearance.
Conclusions
Current research was focused on sustainable old vernacular
architecture's development and tradition continuity aspect.
Multiple criteria approach was proposed for assessment of the whole
building (not for one specific part of the building as in many other
researches). Also, the findings of rational building's
modernisation variant have been made.
It was proposed to apply grey number theory due to its possibility
to use uncertain information, expressed in intervals. For this case
study as uncertain information was considered information related with
thermal insulation materials. TOPSIS Grey method was applied for current
research. AHP method was applied to determine relative significances of
the quantitative and qualitative criteria.
The presented case study of old vernacular building shows that the
rational variant of building's modernisation is when the small
interventions to the building's external appearance are made
seeking to improve thermal performance and daylighting characteristics.
For the current example, thermal insulation was added inside the room of
the building and windows were increased, maintaining their typical
traditional proportions.
Comparing the current and earlier case studies results, it was
concluded that evaluation of one specific part of the building, e.g.
windows, is not the same as the complete evaluation of the whole
building. Modern window solution was the best variant when alternatives
for solving the daylighting problem were ranked (Siozinyte,
Antucheviciene 2013). In this case study according to
experts'opinion the daylighting parameters are less important when
the whole building is evaluated. In their opinion tradition is much
important than current norms when analysing vernacular buildings'
modernization. The established priority order of modernization
alternatives confirmed this attitude.
It is noticed that judgements of the experts are close related with
their intelligence: profession, logic, knowledge about vernacular
architecture, etc. These judgements are quite subjective. For more
objective assessment different methods could be applied.
It can be assumed that it is not enough to evaluate separate parts
of a building, even using a number of criteria for analysis, when making
important decisions, such as vernacular architecture's change. It
is suggested to evaluate upgrading of the whole building simultaneously
and using multiple criteria approach. Also, every evaluated building
should always be considered individually due to its different parameters
(situation in the area, architecture, construction, etc.).
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Egle SIOXINYTE, Jurgita ANTUCHEVICIENE, Vladislavas KUTUT
Department of Construction Technology and Management, Vilnius
Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius,
Lithuania
Received 30 Oct 2013; accepted 28 Feb 2014
Corresponding author: Jurgita Antucheviciene
E-mail: jurgita.antucheviciene@vgtu.lt Egle SIOZINYTE. PhD student
at the Department of Architectural Engineering formerly, and at the
Department of Construction Technology and Management at present, Vilnius
Gediminas Technical University, Lithuania. Research interests:
development of vernacular architecture.
Jurgita ANTUCHEVICIENE. Doctor, Assoc. Professor at the Department
of Construction Technology and Management, Vilnius Gediminas Technical
University, Lithuania. Research interests: sustainable development,
construction business management and investment, multiple criteria
analysis, decision-making theories and decision support systems.
Vladislavas KUTUT. Doctor, Assoc. Professor at the Department of
Construction Technology and Management, Vilnius Gediminas Technical
University, Lithuania. Research interests: implementation of
technological processes and restoration of heritage objects.
Table 1. Criteria for comparison of alternatives
Criteria Units
[x.sub.1] - energy savings through kWh
added extra layer of thermal
insulation for the wall
[x.sub.2] - relationship (ratio) between Times
heat losses and solar energy
inflows through the building
external envelope (walls
and windows)
[x.sub.3] - area of the room when an [m.sup.2]
extra layer of thermal
insulation is added
[x.sub.4] - walls' thermal insulation Points
influence for the whole
building appearance
[x.sub.5] - influence of window change Points
for the whole building
appearance
[x.sub.6] - ratio of building facade part Times
and window glazed surface
area
[x.sub.7] - satisfying the minimal day- Times
lighting regulations
(according to STR
2.02.01:2004): ratio of
minimal required and existing
window glazed surface area
[x.sub.8] - satisfying the building envelope's W/[m.sup.2]K
thermal performance regulations
(according to STR 2.05.01:2005):
heat transfer coefficient of
the wall
[x.sub.9] - satisfying the regulations Points
for building in protected
area (architectural aspect)
[x.sub.10] - reflection of period/era Points
norms, technologies, etc.
Criteria Optimum Alternatives for building renovation
[a.sub.1] [a.sub.2] [a.sub.3]
[x.sub.1] - max 0.00 0.00 0.00
[x.sub.2] - min 81.43 36.00 30.49
[x.sub.3] - max 35.28 35.28 35.28
[x.sub.4] - min 0 0 0
[x.sub.5] - min 1 3 4
[x.sub.6] - max 8.88 3.29 5.17
[x.sub.7] - min 1.89 1.00 0.97
[x.sub.8] - min 0.78 0.78 0.78
[x.sub.9] - max 5 3 1
[x.sub.10] - max 1 2 5
Alternatives for building renovation
Criteria
[a.sub.4] [a.sub.5] [a.sub.6]
[x.sub.1] - [57.74;59.74] [57.74;59.74] [57.74;59.74]
[x.sub.2] - [20.92;22.95] [9.68;10.56] [9.34;10.05]
[x.sub.3] - 35.28 35.28 35.28
[x.sub.4] - 5 5 5
[x.sub.5] - 1 3 4
[x.sub.6] - 8.88 3.29 5.17
[x.sub.7] - 1.89 1.00 0.97
[x.sub.8] - [0.183;0.202] [0.183;0.202] [0.183;0.202]
[x.sub.9] - 4 2 1
[x.sub.10] - 2 3 5
Criteria Alternatives for building renovation
[a.sub.7] [a.sub.8] [a.sub.9]
[x.sub.1] - [57.74;59.74] [57.74;59.74] [57.74;59.74]
[x.sub.2] - [20.92;22.95] [9.68; 10.56] [9.34;10.05]
[x.sub.3] - [27.86;32.48] [27.86;32.48] [27.86;32.48]
[x.sub.4] - 0 0 0
[x.sub.5] - 1 3 4
[x.sub.6] - 8.88 3.29 5.17
[x.sub.7] - 1.89 1.00 0.97
[x.sub.8] - [0.183;0.202] [0.183;0.202] [0.183;0.202]
[x.sub.9] - 5 3 1
[x.sub.10] - 2 3 5
Table 2. Weights of the criteria [w.sub.j]
Criteria
Criteria [x.sub.1] [x.sub.2] [x.sub.3] [x.sub.4] [x.sub.5]
[x.sub.1] 1.0000 1.5976 2.1335 0.8596 1.0443
[x.sub.2] 0.6260 1.0000 1.5474 0.9207 0.9686
[x.sub.3] 0.4687 0.6463 1.0000 0.5596 0.7019
[x.sub.4] 1.1633 1.0861 1.7869 1.0000 1.3098
[x.sub.5] 0.9576 1.0324 1.4247 0.7635 1.0000
[x.sub.6] 0.7199 0.5264 0.9927 0.6420 0.7685
[x.sub.7] 0.6699 0.7654 1.3488 0.8695 1.2287
[x.sub.8] 1.1313 1.6874 2.5690 1.4189 1.5422
[x.sub.9] 1.6265 1.5014 2.1548 1.4085 1.8783
[x.sub.10] 0.6704 0.7330 0.8046 0.5413 0.6420
[w.sub.j] 1158 0.0977 0.0647 0.1120 0.0913
Criteria
Criteria [x.sub.6] [x.sub.7] [x.sub.8] [x.sub.9]
[x.sub.1] 1.5935 1.4927 0.8839 0.6148
[x.sub.2] 1.8998 1.3064 0.5926 0.6660
[x.sub.3] 1.0074 0.7414 0.3893 0.4641
[x.sub.4] 1.5576 1.1501 0.7048 0.7100
[x.sub.5] 1.3012 0.8138 0.6484 0.5324
[x.sub.6] 1.0000 0.6054 0.3973 0.6331
[x.sub.7] 1.6518 1.0000 0.7210 0.7641
[x.sub.8] 2.5168 1.3870 1.0000 1.1892
[x.sub.9] 1.5794 1.3087 0.8409 1.0000
[x.sub.10] 0.9299 0.7731 0.6058 0.6164
[w.sub.j] 0.0678 0.0946 0.1475 0.1395
Criteria
Criteria [x.sub.10]
[x.sub.1]
[x.sub.2] 1.3643
[x.sub.3] 1.2428
[x.sub.4] 1.8476
[x.sub.5] 1.5576
[x.sub.6] 1.0754
[x.sub.7] 1.2935
[x.sub.8] 1.6507
[x.sub.9] 1.6224
[x.sub.10] 1.0000
[w.sub.j] 0.0692
Table 3. Normalised decision-making matrix
Criteria [[bar.x].sub.1] [[bar.x].sub.2] [[bar.x].sub.3]
Alternatives
[a.sub.1] [bar.w] 0000 0.0000 1.0000
[bar.b] 0000 0.0000 1.0000
[a.sub.2] [bar.w] 0.0000 0.5579 1.0000
[bar.b] 0.0000 0.5579 1.0000
[a.sub.3] [bar.w] 0.0000 0.6256 1.0000
[bar.b] 0.0000 0.6256 1.0000
[a.sub.4] [bar.w] 0.9163 0.7182 1.0000
[bar.b] 1.0000 0.7431 1.0000
[a.sub.5] [bar.w] 0.9163 0.8703 1.0000
[bar.b] 1.0000 0.8811 1.0000
[a.sub.6] [bar.w] 0.9163 0.8766 1.0000
[bar.b] 1.0000 0.8853 1.0000
[a.sub.7] [bar.w] 0.9163 0.7182 0.7897
[bar.b] 1.0000 0.7431 0.9206
[a.sub.8] [bar.w] 0.9163 0.8703 0.7897
[bar.b] 1.0000 0.8811 0.9206
[a.sub.9] [bar.w] 0.9163 0.8766 0.7897
[bar.b] 1.0000 0.8853 0.9206
Criteria [[bar.x].sub.4] [[bar.x].sub.5] [[bar.x].sub.6]
[a.sub.1] 1.0000 0.7500 1.0000
1.0000 0.7500 1.0000
[a.sub.2] 1.0000 0.2500 0.3705
1.0000 0.2500 0.3705
[a.sub.3] 1.0000 0.0000 0.5822
1.0000 0.0000 0.5822
[a.sub.4] 0.0000 0.7500 1.0000
0.0000 0.7500 1.0000
[a.sub.5] 0.0000 0.2500 0.3705
0.0000 0.2500 0.3705
[a.sub.6] 0.0000 0.0000 0.5822
0.0000 0.0000 0.5822
[a.sub.7] 1.0000 0.7500 1.0000
1.0000 0.7500 1.0000
[a.sub.8] 1.0000 0.2500 0.3705
1.0000 0.2500 0.3705
[a.sub.9] 1.0000 0.0000 0.5822
1.0000 0.0000 0.5822
Criteria [[bar.x].sub.7] [[bar.x].sub.8] [[bar.x].sub.9]
Alternatives
[a.sub.1] 0.0000 0.0000 1.0000
0.0000 0.0000 1.0000
[a.sub.2] 0.4709 0.0000 0.6000
0.4709 0.0000 0.6000
[a.sub.3] 0.4868 0.0000 0.2000
0.4868 0.0000 0.2000
[a.sub.4] 0.0000 0.7410 0.8000
0.0000 0.7654 0.8000
[a.sub.5] 0.4709 0.7410 0.4000
0.4709 0.7654 0.4000
[a.sub.6] 0.4868 0.7410 0.2000
0.4868 0.7654 0.2000
[a.sub.7] 0.0000 0.7410 1.0000
0.0000 0.7654 1.0000
[a.sub.8] 0.4709 0.7410 0.6000
0.4709 0.7654 0.6000
[a.sub.9] 0.4868 0.7410 0.2000
0.4868 0.7654 0.2000
Criteria [[bar.x].sub.10]
Alternatives
[a.sub.1] 0.2000
0.2000
[a.sub.2] 0.4000
0.4000
[a.sub.3] 1.0000
1.0000
[a.sub.4] 0.4000
0.4000
[a.sub.5] 0.6000
0.6000
[a.sub.6] 1.0000
1.0000
[a.sub.7] 0.4000
0.4000
[a.sub.8] 0.6000
0.6000
[a.sub.9] 1.0000
1.0000
Table 4. Normalised-weighted decision-making matrix
Criteria [[bar.x].sub.1] [[bar.x].sub.2]
Alternatives
[a.sub.1] [bar.w] 0.0000 0.0000
[bar.b] 0.0000 0.0000
[a.sub.2] [bar.w] 0.0000 0.0545
[bar.b] 0.0000 0.0545
[a.sub.3] [bar.w] 0.0000 0.0611
[bar.b] 0.0000 0.0611
[a.sub.4] [bar.w] 0.1061 0.0702
[bar.b] 0.1158 0.0726
[a.sub.5] [bar.w] 0.1061 0.0850
[bar.b] 0.1158 0.0861
[a.sub.6] [bar.w] 0.1061 0.0856
[bar.b] 0.1158 0.0865
[a.sub.7] [bar.w] 0.1061 0.0702
[bar.b] 0.1158 0.0726
[a.sub.8] [bar.w] 0.1061 0.0850
[bar.b] 0.1158 0.0861
[a.sub.9] [bar.w] 0.1061 0.0856
[bar.b] 0.1158 0.0865
Criteria [[bar.x].sub.3] [[bar.x].sub.4] [[bar.x].sub.5]
Alternatives
[a.sub.1] 0.0647 0.1120 0.0684
0.0647 0.1120 0.0684
[a.sub.2] 0.0647 0.1120 0.0228
0.0647 0.1120 0.0228
[a.sub.3] 0.0647 0.1120 0.0000
0.0647 0.1120 0.0000
[a.sub.4] 0.0647 0.0000 0.0684
0.0647 0.0000 0.0684
[a.sub.5] 0.0647 0.0000 0.0228
0.0647 0.0000 0.0228
[a.sub.6] 0.0647 0.0000 0.0000
0.0647 0.0000 0.0000
[a.sub.7] 0.0511 0.1120 0.0684
0.0595 0.1120 0.0684
[a.sub.8] 0.0511 0.1120 0.0228
0.0595 0.1120 0.0228
[a.sub.9] 0.0511 0.0595 0.112 0.0000
0.112 0.0000
Criteria [[bar.x].sub.6] [[bar.x].sub.7] [[bar.x].sub.8]
Alternatives
[a.sub.1] 0.0678 0.0000 0.0000
0.0678 0.0000 0.0000
[a.sub.2] 0.0251 0.0445 0.0000
0.0251 0.0445 0.0000
[a.sub.3] 0.0395 0.0460 0.0000
0.0395 0.0460 0.0000
[a.sub.4] 0.0678 0.0000 0.1093
0.0678 0.0000 0.1129
[a.sub.5] 0.0251 0.0445 0.1093
0.0251 0.0445 0.1129
[a.sub.6] 0.0395 0.0460 0.1093
0.0395 0.0460 0.1129
[a.sub.7] 0.0678 0.0000 0.1093
0.0678 0.0000 0.1129
[a.sub.8] 0.0251 0.0445 0.1093
0.0251 0.0445 0.1129
[a.sub.9] 0.0395 0.046 0.1093
0.0395 0.046 0.1129
Criteria [[bar.x].sub.9] [[bar.x].sub.10]
Alternatives
[a.sub.1] 0.1395 0.0138
0.1395 0.0138
[a.sub.2] 0.0837 0.0277
0.0837 0.0277
[a.sub.3] 0.0279 0.0692
0.0279 0.0692
[a.sub.4] 0.1116 0.0277
0.1116 0.0277
[a.sub.5] 0.0558 0.0415
0.0558 0.0415
[a.sub.6] 0.0279 0.0692
0.0279 0.0692
[a.sub.7] 0.1395 0.0277
0.1395 0.0277
[a.sub.8] 0.0837 0.0415
0.0837 0.0415
[a.sub.9] 0.0279 0.0692
0.0279 0.0692
Table 5. Ideal and negative-ideal solutions
Criteria [[bar.x].sub.1] [[bar.x].sub.2] [[bar.x].sub.3]
[A.sup.w+] 1061 0.0856 0.0647
[A.sup.b+] 1158 0.0865 0.0647
[A.sup.w-] 0000 0.0000 0.0511
[A.sup.b-] 0000 0.0000 0.0595
Criteria [[bar.x].sub.4] [[bar.x].sub.5] [[bar.x].sub.6]
[A.sup.w+] 0.1120 0.0684 0.0678
[A.sup.b+] 0.1120 0.0684 0.0678
[A.sup.w-] 0.0000 0.0000 0.0251
[A.sup.b-] 0.0000 0.0000 0.0251
Criteria [[bar.x].sub.7] [[bar.x].sub.8] [[bar.x].sub.9]
[A.sup.w+] 0.0460 0.1093 0.1395
[A.sup.b+] 0.0460 0.1129 0.1395
[A.sup.w-] 0.0000 0.0000 0.0279
[A.sup.b-] 0.0000 0.0000 0.0279
Criteria [[bar.x].sub.10]
[A.sup.w+] 0.0692
[A.sup.b+] 0.0692
[A.sup.w-] 0.0138
[A.sup.b-] 0.0138
Table 6. Results
Alternatives [a.sub.1] [a.sub.2] [a.sub.3] [a.sub.4]
[L.sup.+.sub.i] 1930 0.1855 0.2079 0.1318
[L.sup.-.sub.i] 1778 0.1464 0.1476 0.2088
[K.sub.i] 4794 0.4410 0.4151 0.6130
Alternatives [a.sub.5] [a.sub.6] [a.sub.7] [a.sub.8]
[L.sup.+.sub.i] 0.1556 0.1746 0.0645 0.0888
[L.sup.-.sub.i] 0.19901 0.1939 0.2479 0.2256
[K.sub.i] 0.5499 0.5262 0.7935 0.7176
Alternatives [a.sub.9]
[L.sup.+.sub.i] 0.1343
[L.sup.-.sub.i] 0.2236
[K.sub.i] 0.6248
