Solving the problems of daylighting and tradition continuity in a reconstructed vernacular building.
Siozinyte, Egle ; Antucheviciene, Jurgita
Introduction
Vernacular architecture should be fully integrated into the modern
life of the community in such a way as to retain local practices and
ways of life (Battaini-Dragoni 2008). When talking about the development
of this architecture, the question remains of how new developments based
on traditional features should look like, which features should remain
and which may be forgotten. Necessarily, we lose something old when
creating something new, but professional innovations always give more
for socium than consuming (Bucas, Mlinkauskiene 2011). It is curious to
see what architecture will tell to the future generations and what
innovative architectural solutions are deemed to be acceptable when
working with new designs based on vernacular architecture features or
while reconstructing the old ones. New layers should represent the
ideas, technology, materials and architectural language of each
generation (Macdonald 2011). There are a number of principles that, if
followed, can result in successful extensions that will preserve, even
enhance, the character of the original building (Oram, Stelfox 2004).
Old vernacular buildings frequently do not satisfy some of the
norms for a contemporary building, and in some cases, we can face the
problems when trying to find the balance between new
requirements/standards and tradition continuity. One of those
encountered in vernacular architecture is that minimal daylighting
parameters determined in building regulations are not always satisfied.
It is also not entirely clear how to find the balance between new
requirements/standards/other norms and old traditions when solving the
daylighting problem.
The issue mentioned above is detected in Lithuanian vernacular
architecture. Vernacular architecture is officially and legally
propagated in the protected areas of the country. In the rest part of
the country there is no directional promotion of this type of
architecture. Moreover, regulations on the protected areas, e.g.
requirements for architecture, and other building regulations intersect
when talking about indoor daylighting (Reglamentation of Protection of
Aukstaitija Region National Park 2002; STR 2.02.01:2004). In some cases,
it is possible to observe the situation when satisfying both regulations
is impossible. Then, the question of how to solve the problem in the
right way arises.
Using Multiple Criteria Decision Making (MCDM) methods assists in
finding rational decisions on various problems. These methods are
applied in different research fields, and one of those presents MCDM
methods applied for building design, construction and development
(Saparauskas et al. 2011; Ogunkah, Yang 2012; Mela et al. 2012; Akadiri
et al. 2013; Kuzman et al. 2013; Tamosaitiene et al. 2013; Zavadskas et
al. 2013a). Also, some researches apply MCDM methods for rural buildings
and their development (Zavadskas, Antucheviciene 2007; Jeong et al.
2012, 2013; Hashemkhani Zolfani, Zavadskas 2013).
Looking for the balance between contemporary norms and tradition
continuity, it is important to evaluate various criteria, such as the
importance of tradition continuity, the use of modern constructions,
materials and techniques, sustainability, health and comfort,
aesthetics, etc. Different researchers analyse the above introduced
aspects of vernacular architecture on an individual basis (van Hoof, van
Dijken 2008; Foruzanmehr, Vellinga 2011; Keizikas et al. 2012; Yuksek,
Esin 2013). The novelty of the current research is a suggestion to use
the multiple criteria approach and analyse several aspects
simultaneously.
The article seeks for actualizing one of the problems of developing
Lithuanian vernacular architecture associated with indoor daylighting.
Also, the aim of this paper is to present possible ways of improving
indoor daylighting for vernacular architecture when trying to save the
tradition and satisfy minimal daylighting norms determined in building
regulations. The problem is evaluated using multiple quantitative and
qualitative criteria. The weight of each criterion is calculated using
the Analytic Hierarchy Process (AHP) method. Possible solutions are
ranked and the best solution identified for the analysed case study
using MCDM methods such as Complex Proportional Assessment (COPRAS),
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
and Weighted Aggregated Sum Product Assessment (WASPAS).
1. Satisfying minimal norms for daylighting in dwellings based on
the features of vernacular architecture
1.1. Existing situation
Daylighting parameters (DP) for dwellings can be evaluated
determining the ratio of the window glazed surface area in the room and
the floor area of the room. STR 2.02.01:2004 regulates minimal
daylighting parameters depending on the type of the room (Table 1) that
must be observed when designing and constructing new buildings.
The condition of DP satisfaction can be checked by determining
minimal required window glazed surface area [A.sub.w min] and comparing
it with the existing window glazed surface area [A.sub.W] in the room:
[A.sub.W] [greater than or equal to] [A.sub.W mm]. (1)
Minimal required window glazed surface area [A.sub.W min] is
evaluated determining the minimal required ratio of the window glazed
surface and room floor area. The study is limited only to the analysis
of DP for living rooms. According to minimal daylighting requirements,
these premises should get the maximum quantity of natural light. The
following calculations are based on the ratio of the window glazed
surface and the room floor area 1:6 (Table 1):
[A.sub.W min] = [A.sub.F]/6, (2)
where [A.sub.F]--the floor area of the room ([m.sup.2]).
The window glazed surface area in room [A.sub.W] is equal to the
sum of the glazed surface areas of each window:
[A.sub.W] = [A.sub.W1] + [A.sub.W2] + ... + [A.sub.Wn], (3)
or, if all windows in the room have the same dimensions
[A.sub.W] = [A.sub.W1] x n, (4)
where n is the number of windows in the room.
[FIGURE 1 OMITTED]
Figure 1 illustrates the change of proportions depending on the
window glazed surface and window frame area, when different types of
frames exist. For example, on a typical vernacular six-part window, the
frame occupies about 50 percent of the total window area; on a
three-part window, the frame occupies about 30 percent.
Checking a minimal DP condition for the room is presented in Table
2 where a room in a building of typical vernacular architecture is
analysed. The area of the room having 6 windows (0.7 x 1.0 m) is 36.00
[m.sup.2]. Four possible variants of windows with different proportions
of the window glazed surface area and frame area are taken into
consideration.
The differences between the minimal required and existing window
glazed surface area for the room are rather significant in all presented
cases (Table 2). Also, it should be noted that the condition presented
in Eqn (1) is not satisfied in any case. Even at 100 percent of window
glazing (dimension of windows makes 0.7 x 1.0 m), it is impossible to
satisfy minimal DP parameters described in regulations when a defined
type of premises is analysed.
The problem is also illustrated by checking how daylighting
parameters meet the current regulations in the old vernacular
architecture of Lithuania. Five dwellings with different parameters
(different window glazed surface area and floor area) characteristic of
different Lithuanian ethnographic regions, including Aukstaitija,
Dzukija, Suvalkija (Suduva), Zemaitija and Mazoji Lietuva (Dubiciai
1989; Kacinskaite et al. 2008; Seselgis et al. 1965) were chosen. They
are presented as A, B, C, D and E types of building, respectively in
Table 3.
The calculations of this research are assumed that window glazed
surface area [A.sub.W1] is equal to the whole window area, with no
taking into account a frame area. Accordingly, the results (Table 3)
show the situation disclosing better conditions (with bigger window
glazed surface area) than those in reality.
The results in Table 3 indicate that all analysed cases do not
satisfy norms required for building regulations. The maximum difference
between the minimal required and existing window glazed surface area of
the room is about 4 times in B-type dwelling with the room area of 15.36
[m.sup.2] and with 1 window having the dimensions of 0.7 x 1.0 m. This
means that the window glazed surface area should be enlarged about 4
times. The smallest difference can be attributed to E-type dwelling with
the room area of 14.28 m and 2 windows with the dimensions of 1.0 x 1.2
m. This room, with the chosen condition for research, satisfies a
minimal DP condition (Eqn (1)); however, it should be noted that
calculations are performed in better conditions then they really are,
i.e. without taking into account the area of frames. Consequently, the
condition is not satisfied.
Living rooms of dwellings should meet at least minimum daylighting
requirements to insure the quality of the life of residents. This can be
done by increasing the window glazed surface area, which would mean the
enlargement of windows or an increase in the quantity of windows.
However, in some cases, under the circumstances of a typical building of
vernacular architecture, it can be hardly achieved. Then, the question
is how the compromise between meeting the current building standards and
keeping the continuity of vernacular architecture can be achieved.
1.2. Possible ways of solving the problem of daylighting
There could be a few possible variants on solving the problem of
daylighting using architectural solutions to the new buildings based on
the features of vernacular architecture or reconstructing old vernacular
buildings: 1) increasing the size of windows while maintaining typical
traditional proportions; 2) increasing the size of windows by changing
the proportion of window height and width; 3) increasing the quantity of
windows; 4) using new glass structures for building facades, as much as
possible trying to maintain the traditional appearance of vernacular
architecture; 5) using new glass structures for building facades, more
or less changing the traditional appearance of vernacular architecture.
The proportions or dimensions of typical traditional windows are
given in literature about Lithuanian vernacular architecture: window
width and height proportion--0.7 x 1.0 m or 0.8 x 1.0 m (Andriusyte et
al. 2008; Bertasiute et al. 2009), more specific dimensions -0.7 x 1.0 m
and 0.8 x 1.0 m (Bertasiute et al. 2008; Seselgis et al. 1965). In some
cases, windows can reach the dimensions of L0 x 1.2 m (Seselgis et al.
1965). Windows are usually divided into several parts (3-6 or even more
parts).
The first from the possible solutions, i.e. increasing the window
size while maintaining typical traditional proportions, may not always
be perfectly adapted. It is difficult to ensure satisfying the norms
required in building regulations and saving traditional features of
vernacular architecture at the same time. A window can be proportionally
enlarged only up to a certain limit, which, in each case of the
building, can be very individual due to the parameters of the whole
building. The windows that are bigger than 1.5 m in height actually
become difficult to implement according to the whole building structure.
There could be not enough space to put ceiling beams on load-bearing
walls. Moreover, the windows could be covered with roof eaves. To avoid
these problems, it could be possible to increase the height of the room.
However, any increase in dwelling parameters makes changes in the
proportions of the whole building or individual parts and therefore in
the overall appearance of dwelling.
The other ways to solve daylight problems using architectural
solutions to new dwellings based on vernacular architecture, such as
increasing the window size by changing the proportion of window height
and width or increasing the quantity of windows, also seem to be quite
problematic.
Changing proportions is contradictory to the intention of saving
traditional forms of vernacular architecture. This means that a new kind
of windows can appear.
Increasing the quantity of windows in dwellings is not the best
choice, and therefore it is not always possible to implement it.
According to the results mentioned above, seeking to satisfy minimal
norms required in building regulations, the quantity of windows should
be increased up to several times. One or two additional windows could
fit into the overall composition of the building. Nevertheless, in case
of more windows, facades may seem unusually and, certainly, not typical
of the vernacular building. From an aesthetic point of view, this might
not be a good solution.
Using new glass structures for building facades is also possible.
Foreign experience (United Kingdom, Ireland, Norway, etc.) shows that
old traditions can be well extended referring to new contemporary
architecture, maintaining a country-specific style, taking over a number
of characteristic features and the rest adapting for today's needs
and standards as well as making modernisation. Even in the protected
areas, it is possible to use the latest architectural solutions (New
Forest National Park Local Development Framework 2011). The usage of new
modern solutions commits a message to the future generations about the
age/time technologies, aesthetical norms, etc. of this period.
Also, a window is an important architectural element when talking
about thermal characteristics of the building. The window has an impact
on the efficiency of house energy. Glass structures, such as windows
with a large glazed surface area at the south facade (direct gain
windows), attached sunspaces, atriums and other modern solutions help
with making energy savings in the passive way (Chwieduk 2004; Sadineni
et al. 2011; Su 2011).
2. Evaluation of a rational solution analysing daylighting in the
reconstructed vernacular building and the problem of tradition
continuity
2.1. MCDM methods applied for ranking alternative solutions
The methods evaluate decision matrix X, which refers to n
alternatives that are evaluated in terms of m criteria. Suppose, there
is the initial decision-making matrix:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
where m is the number of criteria and n is the number of
alternatives. Member [x.sub.ij] denotes the performance measure of the
j-th alternative in terms of the i-th criterion, i = 1, ..., m; j = 1,
..., n.
The relative significances (or weights) of criteria are calculated
applying the AHP method. Then, the weighted normalized decision-making
matrices are formed, the relative significance of alternatives is
calculated applying COPRAS, TOPSIS and WASPAS methods, the ranking order
of alternative solutions is established and the utility degree of every
alternative is calculated and compared.
2.1.1. Complex Proportional Assessment (COPRAS)
The method is presented with reference to Zavadskas and Kaklauskas
(1996) and Antucheviciene et al. (2011, 2012).
To eliminate the units of criterion functions, the method under
discussion uses the following equation:
[[bar.x].sub.ij] = [x.sub.ij]/[n.summation over (j=1)] [x.sub.ij],
(6)
where [[bar.x].sub.ij] is the normalized weighted value of each
criterion, i = 1, ..., m; j = 1, ..., n.
The weighted normalized value [[??].sub.ij] is calculated as:
where [w.sub.i] is the weight of the i-th criterion. In this
particular case, it can be determined by applying the AHP, as described
hereafter in Section 2.1.4.
The normalized weighted value of each i-th criterion belongs to
benefit criteria or cost/loss criteria. Accordingly, the j-th
alternative is then described by maximizing indices [[??].sup.+.sub.ij],
i = 1, ..., m, where i is associated with benefit criteria, and
minimizing indices [[??].sup.-.sub.ij], i = 1, ..., m, where i is
associated with cost/loss criteria.
The sums of weighted normalized maximizing and minimizing indices
[S.sup.+.sub.j] and [S.sup.-.sub.j], respectively, are calculated as
follows:
[S.sup.+.sub.j] = [m.summation over (i=1)] [[??].sub.ij],
[S.sup.-.sub.j] = [m.summation over (i=1)] [[??].sup.-.sub.ij]. (8)
Next, the relative significance [Q.sub.j] of each alternative is
determined:
[Q.sub.j] = [m.summation over (i=1)] [[??].sup.+.sub.ij],
[S.sup.-.sub.j] = [m.summation over (i=1)] [[??].sup.-.sub.ij]. (9)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The priorities of alternatives are defined according to the
preference order of [Q.sub.j].
Utility degree [N.sub.j] is calculated:
[N.sub.j] = [[Q.sub.j]/[Q.sub.max]] 100%, (10)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
2.1.2. Technique for Order Preference by Similarity to Ideal
Solution (TOPSIS)
The method is presented with reference to Hwang and Yoon (1981),
Triantaphyllou (2000) and Antucheviciene et al. (2011, 2012).
TOPSIS uses vector normalization:
[[bar.x].sub.ij] = [x.sub.ij]/[square root of [n.summation over
(j=1)][x.sup.2.sub.ij]], (11)
where [[bar.x].sub.ij] is the normalized value, i = 1, ..., m; j =
1, ..., n.
The weighted normalized value [[??].sub.ij] is calculated according
to Eqn (7).
Ideal and negative-ideal solutions denoted as [A.sup.+] and
[A.sup.-] respectively are defined as follows:
[A.sup.+] = {[[??].sup.+.sub.1], [[??].sup.+.sub.2], ...,
[[??].sup.+.sub.m]}; (12)
[A.sup.-] = {[[??].sup.-.sub.1], [[??].sup.-.sub.2], ...,
[[??].sup.-.sub.m]}, (13)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], if the
i-th criterion represents benefit; [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], if the i-th criterion represents cost/loss.
The Euclidean distance method is then applied to measure the
distances of each alternative from the ideal solution and negative-ideal
solution:
[S.sup.+.sub.j] = [m.summation over (i=1)] [([[??].sub.ij] -
[[??].sup.+.sub.i]).sup.2]; (14)
[S.sup.-.sub.j] = [m.summation over (i=1)] [([[??].sub.ij] -
[[??].sup.- .sub.i]).sup.2]], (15)
where [S.sup.+.sub.j] is the distance from the ideal solution and
[S.sup.- .sub.j] is the distance from the negative-ideal solution, i =
1, ..., m; j = 1, ..., n.
The relative significance of each alternative [Q.sub.j] is defined
as follows:
[Q.sub.j] = [S.sup.-.sub.j]/[S.sup.+.sub.j] + [S.sup.-.sub.j], 0
[less than or equal to] [Q.sub.j] [less than or equal to] 1, j = 1, ...,
n (16)
The best alternative can be found according to the preference order
of [Q.sub.j]. Utility degree [N.sub.j] can be calculated applying Eqn
(10).
2.1.3. Weighted Aggregated Sum Product Assessment (WASPAS)
The method was developed by Zavadskas et al. (2012) and applied for
dealing with civil engineering problems by Zavadskas et al. (2013a, b).
The linear normalization of the initial criteria values [x.sub.ij]
is applied, and dimensionless values [[bar.x].sub.ij] are obtained:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (17)
if [max.sub.j] [x.sub.ij] value is preferable or:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (18)
if [min.sub.i] [x.sub.j] value is preferable.
The relative significance of each alternative [Q.sub.j] is
calculated applying the joint generalized criterion of the weighted
aggregation of additive and multiplicative methods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (19)
where [[lambda].sub.j] is the weighted coefficient.
If [m.summation over (i=1)] [[bar.x].sub.ij][w.sub.i] =
[Q.sup.(1).sub.j], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII], then, the optimal values of weighted coefficient
[[lambda].sub.j] can be calculated when finding minimum dispersion
[[sigma].sup.2] ([Q.sub.j]) and to assure the maximal accuracy of
measurement respectively. The extreme of the function can be found when
the derivative of Eqn (19), in regard to [lambda], is equated to zero:
[[lambda].sub.j] =
[[sigma].sup.2]([Q.sup.(2).sub.j])/[[sigma].sup.2]([Q.sup.(1).sub.j]) +
[[sigma].sup.2]([Q.sup.(2).sub.j]). (20)
Variances [[sigma].sup.2] ([Q.sup.(1).sub.j]) and [[sigma].sup.2]
([Q.sup.(2).sub.j]) should be calculated as:
[[sigma].sup.2] ([Q.sup.(1).sub.j]) = [m.summation over (i=1)]
[w.sup.2.sub.i][[sigma].sup.2]([[bar.x].sub.ij])); (21)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)
In the case of a normal distribution of the initial data with
credibility q = 0.05, the estimates of the variances of the values of
normalized criteria are calculated as follows:
[[sigma].sup.2] ([[bar.x].sub.ij]) =
[(0.05[[bar.x].sub.ij]).sup.2]. (23)
Alternatives can be ranked according to [Q.sub.j] (Eqn (19)).
Utility degree [N.sub.j] can be calculated applying Eqn (10).
2.1.4. Analytic Hierarchy Process (AHP)
The AHP was introduced by Saaty (1980). This method is based on
pairwise comparisons and can be helpful in determining importance
(weight [w.sub.i]) of each criterion.
[FIGURE 2 OMITTED]
The decision-maker has to express his opinion about the value of
every single pairwise comparison of criteria in the linguistic form.
Comparisons are quantified using a scale of a discrete set of numbers.
In the current case, the intensity of importance is measured from 1 to
4. According to this scale, the available values of pairwise comparisons
are the members of the set: {4, 3, 2, 1, 1/2, 1/3, 1/4}. Then, the
pairwise comparison matrix and eigenvector are derived. Next, the
numbers are normalized and the weights of each criterion [w.sub.i] are
specified.
One of the advantages of the AHP methodology is that it allows for
slightly non-consistent pairwise comparisons. In the AHP, pairwise
comparisons in a judgment matrix are considered to be adequately
consistent if the corresponding Consistency Ratio (CR) is less than 10
percent (Saaty 1980). The CR is estimated using Random Consistency Index
(RCI) and calculated Consistency Index (CI). RCI depends on the number
of criteria m (Triantaphyllou, Mann 1995). Consistency Index is
calculated by the formula CI = ([[lambda].sub.max] - m)/(m-1) where
[[lambda].sub.max] is the approximated maximum eigenvalue. Then, the
Consistency Ratio is estimated as CI/RCI.
2.2. Alternatives and criteria for solving the problems of
daylighting in the reconstructed vernacular building and tradition
continuity
For the case study, as an example, a vernacular dwelling from
Aukstaitija region, Lithuania (Fig. 2) was chosen. There are three
possible solutions (alternatives) to improving daylighting of the
analysed vernacular building: [a.sub.1]--increasing the window size
while maintaining typical traditional proportions (Fig. 3 a);
[a.sub.2]--increasing the quantity of windows (Fig. 3b);
[a.sub.3]--using new glass structures for building facades (modern
solution) (Fig. 3c).
The criteria are evaluated using quantitative ([x.sub.1],
[x.sub.3]) and qualitative ([x.sub.2], [x.sub.4], [x.sub.5], [x.sub.6])
measures. Qualitative measures are evaluated using the five-level Likert
item scale (Table 4). Quantitative measures use the results from
research on window daylighting. However, it is noted, that the window
glazed surface area is not equal to the whole window area like it was
presumed in Section 1.2. Hence, window frames are considered when
calculating the glazed surface area.
Criteria for a comparison of possible solutions are presented in
Table 5.
[FIGURE 3 OMITTED]
2.3. Calculation results
The weights of criteria [W.sub.j] are determined applying the AHP
method (Table 6).
The Consistency Ratio coefficient is calculated as follows (for
used methodology, see Section 2.1.4): 1) [[lambda].sub.max] = 6.63; 2)
CI = 0.13; 3) RCI = 1.24; 4) CR = 0.10.
As the Consistency Ratio does not exceed 10 percent, pairwise
comparisons can be considered consistent. Consequently, the estimated
weights of criteria can be used for future calculations when evaluating
alternatives.
Ranking alternatives by applying COPRAS, TOPSIS and WASPAS methods
(Eqns (5)-(23)) is presented in Tables 7-9.
According to calculation results applying COPRAS, TOPSIS and WASPAS
methods, the alternatives are ranked as [a.sub.3] [??] [a.sub.2] [??]
[a.sub.1].
In the case study, the best alternative is the third one (modern
solution, namely using new glass structures for building facades), and
the first alternative is ranked as the worst (increasing the window size
while maintaining typical traditional proportions), whereas the
suggestion to increase the quantity of windows takes the middle
position.
The third alternative is an obvious leader when applying all MCDM
methods used for the current research. Its degree of utility exceeds the
second ranked alternative from 29 percent (according to the results of
WASPAS) to 41 percent (according to the results of TOPSIS) while
differences in the utility degree of the rest two alternative solutions
are rather similar. Their differences are only 5-8 percent. Accordingly,
the rationality of their implementation is almost equal. It is estimated
that using the proposed new glass structures for building facades is the
best compromise solution to satisfying daylighting demands and
preserving the features of vernacular architecture in the above analysed
case.
Conclusions
The multiple criteria approach was proposed for analysing one of
the problems of vernacular architecture, namely daylighting, and looking
for the balance between norms for a contemporary building and tradition
continuity. The problem was evaluated using multiple quantitative and
qualitative measurements.
It was proposed to determine the relative significances of criteria
applying the Analytic Hierarchy Process (AHP) and to find a rational
solution to the problem using Complex Proportional Assessment (COPRAS).
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
and Weighted Aggregated Sum Product Assessment (WASPAS).
The presented case study on indoor daylighting in Lithuanian
vernacular architecture shows that the rational solution to improving
daylighting in a reconstructed building and saving traditional features
of vernacular architecture could be used in new glass structures, such
as large glazed surface area windows, especially in the South facade of
the building, that can be visible or partially hidden, e.g. recessed and
sub-divided.
The other alternatives, such as increasing the size or quantity of
windows, are almost similar (differ about 5-8 percent) and fall behind
from the rational solution from 29 to 41 percent.
The same methods might be adopted for solving other vernacular
architecture problems associated with the compatibility possibilities of
tradition continuity and norms for a contemporary building.
doi: 10.3846/13923730.2013.851113
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http://dx.doi.org/10.5755/j01.eee.122.6.1810
Egle SIOZINYTE, Jurgita ANTUCHEVICIENE
Department of Construction Technology and Management, Vilnius
Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius,
Lithuania
Received 27 Jun 2013; accepted 19 Jul 2013
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.
Table 1. Minimal daylighting parameters depending on the
type of the room (according to STR 2.02.01:2004)
Premises where daylighting Minimal window glazed
is obligatory surface and room floor
area ratio required
Entrance tambour; stairwell hall; 1:19
common use corridors of the house 1:12
Living rooms 1:6
Kitchen 1:8
Living rooms and kitchen daylighted
through windows on the inclined 1:10
roof plane
Table 2. Difference between the minimal required and
existing window glazed surface area of the room
Floor area of Quantity of Proportions Window glazed
the room windows in of the window surface area
[A.sub.F], the room n, glazed [A.sub.wl]
([m.sup.2]) (qty) surface and when window
frame area measurements
when window are 0.7 x 1.0
measurements m,
are 0.7 x 1.0 ([m.sup.2])
m
36.00 6 50:50 0.35
70:30 0.49
85:15 0.595
100:0 0.70
Floor area of Window glazed Minimal Difference
the room surface area window glazed between
[A.sub.F], in the room surface area [A.sub.w] and
([m.sup.2]) [A.sub.W], of the room [A.sub.W min]
([m.sup.2]) [A.sub.W (times)
min],
([m.sup.2])
36.00 2.10 6.00 2.86
2.94 2.04
3.57 1.68
4.20 1.43
Table 3. The minimal required and existing window glazed
surface area of the room
Building Floor area Quantity Sizes of Window
type of the of windows windows in glazed
room in the the room, surface
[A.sub.F], room n, (m) area *
([m.sup.2]) (qty) [A.sub.WI],
([m.sup.2])
A 35.28 5 0.7x1.0 0.70
35.28 4
B 42.25 4 0.7x1.0 0.70
15.36 1
C 40.88 5 0.8x1.0 0.80
31.36 3
14.08 2
10.73 1
9.86 1
D 21.60 2 0.7x1.0 0.70
18.90 2
15.40 2
12.74 2
6.76 1
E 19.04 2 1.0x1.2 1.20
14.28 2
12.58 1
11.56 1
8.70 1
Building Floor area Window Minimal Difference
type of the glazed window between
room surface glazed [A.sub.W]
[A.sub.F], area in surface and
([m.sup.2]) the room area of [A.sub.Wmin],
[A.sub.W], the room (times)
([m.sup.2]) [A.sub.W
min],
([m.sup.2])
A 35.28 3.50 5.88 1.68
35.28 2.80 5.88 2.10
B 42.25 2.80 7.04 2.51
15.36 0.70 2.56 3.66
C 40.88 4.00 6.81 1.70
31.36 2.40 5.23 2.18
14.08 1.60 2.35 1.47
10.73 0.80 1.79 2.24
9.86 0.80 1.64 2.05
D 21.60 1.40 3.60 2.57
18.90 1.40 3.15 2.25
15.40 1.40 2.57 1.83
12.74 1.40 2.12 1.52
6.76 0.70 1.13 1.61
E 19.04 2.40 3.17 1.32
14.28 2.40 2.38 0.99
12.58 1.20 2.10 1.75
11.56 1.20 1.93 1.61
8.70 1.20 1.45 1.21
* window glazed surface area [A.sub.W1] is equal to the
whole window area.
Table 4. The scale evaluating qualitative criteria
Scale Criteria
[x.sub.2], [x.sub.6]
[x.sub.4], [x.sub.5]
1 very weak very unattractive
2 weak unattractive
3 medium medium
4 strong attractive
5 very strong very attractive
Table 5. Criteria for comparing alternatives
Criteria Units Optimum
[x.sub.1]- satisfying Times min
minimal
daylighting
regulations
(according to
STR
2.02.01:2004):
the ratio of
the minimal
required and
existing window
glazed surface
area
[x.sub.2]- satisfying Points max
regulations on
the building in
protected areas
[x.sub.3]- ratio of a part Times max
of the building
facade and
window glazed
surface area
[x.sub.4]- influence of a Points min
changed window
on the whole
building
appearance
[x.sub.5]- reflection of Points max
period/era
norms,
technologies,
etc.
[x.sub.6]- aesthetics Points max
Criteria Alternatives for
daylighting problem solution
[a.sub.1] [a.sub.2] [a.sub.3]
[x.sub.1]- satisfying 1.89 1.00 0.97
minimal
daylighting
regulations
(according to
STR
2.02.01:2004):
the ratio of
the minimal
required and
existing window
glazed surface
area
[x.sub.2]- satisfying 5 3 1
regulations on
the building in
protected areas
[x.sub.3]- ratio of a part 8.88 3.29 5.17
of the building
facade and
window glazed
surface area
[x.sub.4]- influence of a 1 3 4
changed window
on the whole
building
appearance
[x.sub.5]- reflection of 1 2 5
period/era
norms,
technologies,
etc.
[x.sub.6]- aesthetics 1 1 5
Table 6. The weights of criteria [w.sub.j] applying
the AHP method
Criteria
[x.sub.1] [x.sub.2] [x.sub.3]
Criteria
[x.sub.1] 1/1 1/1 4/1
[x.sub.2] 1/1 1/1 3/1
[x.sub.3] 4 3 11/
[x.sub.4] 1 3 4 2/
[x.sub.5] 1/3 4/1 3/1
[x.sub.6] 1/2 1/1 4/1
[w.sub.j] 0.287 0.175 0.050
Criteria
[x.sub.4] [x.sub.5] [x.sub.6]
Criteria
[x.sub.1] 3/1 3/1 2/1
[x.sub.2] 4/1 1/4 1/1
[x.sub.3] 1 2 13/ 4
[x.sub.4] 1/ 2 4
[x.sub.5] 2/1 1/1 1/1
[x.sub.6] 4/1 1/1 1/1
[w.sub.j] 0.070 0.233 0.186
Table 7. Ranking alternatives by applying the COPRAS method
Normalised decision-making matrix
Criteria [[bar.x].sub.1] [[bar.x].sub.2]
Alternatives [a.sub.1] 0.490 0.556
[a.sub.2] 0.259 0.333
[a.sub.3] 0.251 0.111
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives [a.sub.1] 0.140 0.097
[a.sub.2] 0.074 0.058
[a.sub.3] 0.072 0.019
Criteria [[bar.x].sub.3] [[bar.x].sub.4]
Alternatives [a.sub.1] 0.512 0.125
[a.sub.2] 0.190 0.375
[a.sub.3] 0.298 0.500
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives [a.sub.1] 0.026 0.009
[a.sub.2] 0.010 0.026
[a.sub.3] 0.015 0.035
Criteria [[bar.x].sub.5] [[bar.x].sub.6]
Alternatives [a.sub.1] 0.125 0.143
[a.sub.2] 0.250 0.143
[a.sub.3] 0.625 0.714
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives [a.sub.1] 0.029 0.027
[a.sub.2] 0.058 0.027
[a.sub.3] 0.145 0.133
Results
Maximizing Minimizing
indices indices
[S.sup.+.sub.j] [S.sup.-.sub.j]
Alternatives [a.sub.1] 0.179 0.149
[a.sub.2] 0.153 0.100
[a.sub.3] 0.313 0.107
Results
Relative Utility
significance degree
[Q.sub.j] [N.sub.j]
Alternatives [a.sub.1] 0.270 61
[a.sub.2] 0.289 66
[a.sub.3] 0.441 100
Table 8. Ranking alternatives applying the TOPSIS method
Normalised decision-making matrix
Criteria [[bar.x].sub.1] [[bar.x].sub.2]
Alternatives
[a.sub.1] 0.805 0.845
[a.sub.2] 0.426 0.507
[a.sub.3] 0.413 0.169
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives
[a.sub.1] 0.231 0.148
[a.sub.2] 0.122 0.089
[a.sub.3] 0.118 0.030
Ideal and negative-ideal solutions
Criteria [[??].sub.1] [[??].sub.1]
[A.sup.+] 0.118 0.148
[A.sup.-] 0.231 0.030
Criteria [[bar.x].sub.3] [[bar.x].sub.4]
Alternatives
[a.sub.1] 0.823 0.196
[a.sub.2] 0.305 0.588
[a.sub.3] 0.479 0.785
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives
[a.sub.1] 0.041 0.014
[a.sub.2] 0.015 0.041
[a.sub.3] 0.024 0.055
Ideal and negative-ideal solutions
Criteria [[??].sub.1] [[??].sub.1]
[A.sup.+] 0.041 0.014
[A.sup.-] 0.015 0.055
Criteria [[bar.x].sub.5] [[bar.x].sub.6]
Alternatives
[a.sub.1] 0.183 0.193
[a.sub.2] 0.365 0.193
[a.sub.3] 0.913 0.962
Normalised-weighted decision-making matrix
Criteria [[??].sub.1] [[??].sub.1]
Alternatives
[a.sub.1] 0.043 0.036
[a.sub.2] 0.085 0.036
[a.sub.3] 0.212 0.179
Ideal and negative-ideal solutions
Criteria [[??].sub.1] [[??].sub.1]
[A.sup.+] 0.212 0.179
[A.sup.-] 0.043 0.036
Results
Distance Distance from
from ideal negative-ideal
solution solution
[S.sup.+.sub.j] [S.sup.-.sub.j]
Alternatives
[a.sub.1] 0.249 0.128
[a.sub.2] 0.204 0.132
[a.sub.3] 0.126 0.249
Results
Relative Utility
significance degree
[N.sub.j]
Alternatives
[a.sub.1] 0.339 51
[a.sub.2] 0.392 59
[a.sub.3] 0.664 100
Table 9. Ranking alternatives applying the WASPAS method
Normalised decision-making matrix
Criteria [[bar.x].sub.1] [[bar.x].sub.2]
Alternatives
[a.sub.1] 0.513 1.000
[a.sub.2] 0.970 0.600
[a.sub.3] 1.000 0.200
Normalised-weighted decision-making matrix for
Criteria [[??].sub.1] [[??].sub.2]
Alternatives
[a.sub.1] 0.147 0.175
[a.sub.2] 0.278 0.105
[a.sub.3] 0.287 0.035
Normalised-weighted decision-making matrix for [Q.sup.(2).sub.j]
Criteria [[??].sub.1] [[??].sub.2]
Alternatives
[a.sub.1] 0.826 1.000
[a.sub.2] 0.991 0.915
[a.sub.3] 1.000 0.755
Criteria [[bar.x].sub.3] [[bar.x].sub.4]
Alternatives
[a.sub.1] 1.000 1.000
[a.sub.2] 0.371 0.333
[a.sub.3] 0.582 0.250
Normalised-weighted decision-making matrix for
Criteria [[??].sub.3] [[??].sub.4]
Alternatives
[a.sub.1] 0.050 0.070
[a.sub.2] 0.019 0.023
[a.sub.3] 0.029 0.017
Normalised-weighted decision-making matrix for [Q.sup.(2).sub.j]
Criteria [[??].sub.3] [[??].sub.4]
Alternatives
[a.sub.1] 1.000 1.000
[a.sub.2] 0.951 0.927
[a.sub.3] 0.973 0.908
Criteria [[bar.x].sub.5] [[bar.x].sub.6]
Alternatives
[a.sub.1] 0.200 0.200
[a.sub.2] 0.400 0.200
[a.sub.3] 1.000 1.000
Normalised-weighted decision-making matrix for
Criteria [[??].sub.5] [[??].sub.6]
Alternatives
[a.sub.1] 0.047 0.037
[a.sub.2] 0.093 0.037
[a.sub.3] 0.233 0.186
Normalised-weighted decision-making matrix for [Q.sup.(2).sub.j]
Criteria [[??].sub.5] [[??].sub.6]
Alternatives
[a.sub.1] 0.6876 0.741
[a.sub.2] 0.8080 0.741
[a.sub.3] 1.0000 1.000
Results
Optimal Relative Utility
[[lambda].sub.j] significance degree
[Q.sub.j] [N.sub.j]
Alternatives
[a.sub.1] 0.434 0.428 65
[a.sub.2] 0.410 0.472 71
[a.sub.3] 0.423 0.662 100
