Copras based comparative analysis of the European country management capabilities within the construction sector in the time of crisis/Europos valstybiu gebejimo valdyti statybos sektoriu krizes laikotarpiu palyginamoji analize taikant copras metoda.

Kildiene, Simona ; Kaklauskas, Arturas ; Zavadskas, Edmundas Kazimieras 等

1. Introduction

Strategically important construction sector includes designing of buildings, formation of the infrastructure connecting the whole economic sectors. This sector is named as the most important employer, it makes the great contribution to the common capital of European countries. Construction is one of the biggest industries in Europe it takes 10 percents of GDP and requires 50.5 percents of the capital investment. The construction sector employes over 12 millions of European citizens and involves 26 millions to the particular sphere of the construction industry DKM Economic Consultants (2010).

In comparison with other economic sectors the construction importance depends on the different factors. According to Kaklauskas et al. (2011) construction efficiency at most depends on certain number of variables at macro level and micro level. The costs of the ground area, design process, construction process, business competition, efficiency level of enterprises etc. are possibly at micro level. At macro level economic, politic, legal, technological, cultural and natural environments have an impact on the construction. Thus, construction sector depends on the set global and local factors which cause certain swings in the economic activity both in construction and other industrial branches.

You can notice that the relationship between construction section and economy was studied by lots of scientists (Giang and Pheng 2010; Pellicer et al. 2009; Khan 2008; Wigrena and Wilhelmsson 2007; Chiang et al. 2006; You and Zi 2007). For example, Pellicer et al. (2009) analyzed the effect of decay on the construction sector in terms of macroeconomics. Authors used regression model for study and forecast of the situation in construction sector. Chiang et al. (2006) used the tables of the model "input-output (i-o)" for study of the construction sector in macroeconomics terms. This model is efficient instrument for determination of effect of macroeconomic factors on the construction and construction forecasting. Giang and Pheng (2010) carried out theoretical study of construction role on the economy in accordance with three scenario: (a) Infrastructure is adequate for economic growth when the infrastructure is built ahead, then the business activities of other goods and services that the infrastructure helps create come into place; (b) Infrastructure becomes excessive when the infrastructure is constructed ahead as planned, but then an unexpected economic downturn occurs; and (c) Infrastructure is inadequate to support economic growth when there is an unexpected economic upturn. Khan et al. (2008) analyzed the relation between construction sector and GDP (gross domestic product) in 1950-2005. In Pakistan Granger causality test is used (Granger and Newbold 1974). To calculate the reliability of relations and results the Unit Root tests based on time series and Co-integration test were applied. Economic time series--is sequential array of the values of economic variables. Weekly, monthly, annual indexes of productions, costs, income, population size, labour power, gross domestic product (GDP) are examples of economic time series. Obtained results of the investigations show that there is a strong causal relation between economy and construction sector. Two types of econometric models (cointegration and error correction) were applied by Wigren and Wilhelmsson for investigations of construction market in the Western Europe (2007). After analyzing criteria characterized the construction sector of fourteen countries of the Western Europe it was concluded that investments in residential and non-residential building construction or in construction of other buildings have both direct and indirect impacts on economic growth. These investigations also detected that there is a strong relationship between infrastructure and economic productivity, particularly residential building construction has a long-term effect on the economic growth. You and Zi (2007) analyzed the construction industry development in Korea (in 1996-2000) for various periods of the crisis using the method of data environment analysis (DEA). By this method some important factors which delay efficiently of construction enterprises in crisis period were determined. The European construction sector at micro level was investigated by Proverbs and Holf (2000), Proverbs et al. (1999). Chateau (2007), Mymrin and Correa (2007), Knoepfel (1992) and other wrote about the market of construction products in Europe.

The European construction market is non-homogenous. The current situation of each member state and perspectives depend on state position taking into account needs, demographic trends, and main economic principles etc. Economic environment in the country affects directly on business. Economic environment is determined by the tax and financial resources policy, capital flow, investment environment, loaning and rate of interest implemented by state bodies. The situation depends also on when corrections of immovable property market were performed and economic openness of individual country for the impact of the financial and economic crisis. And finally it depends on what long-term measures of recovery will be selected and how successfully they will affect on the construction sector (Kaklauskas et al. 2010a). Certain industry branches are characterized by cyclical swing covered changes of production, work, and sales number. Among these branches there are such sectors as construction, steel industry, and aero industry. The ordinary swings of construction product values reach about 20 percent. It was noticed that cyclical swings in construction industry which appear as "booms" and recession are recurred (Kaklauskas et al. 2011).

Clear and reliable access to statistic data is very important while performing the monitoring of construction sector market. In this document collected data characterize the construction sector market of 23 European states in 2009. The data obtained from Eurostat (2010) and European Federation of Building and Woodworkers (2010) database demonstrate percent change of construction indexes in comparison with ones in 2008. The data describe six criteria affecting the market of the construction sector: GDP change, index of growth rate of buildings and all construction products, number of issued construction permits for new residential buildings, price index change for civil engineering products, price index change for new residential building construction, total employment in construction sector. 23 European countries, for which specific indexes were found, were selected for evaluation.

2. Determination of important entropy-based criteria

For achievement of the goal specified in this article, first of all the calculations were performed in order to determine criteria importance by entropy method. The initiator of the method (Shannon 1948) gave the following numerical expression of entropy method (1) (quantity of information in dataset):

S = 1/N [summation over (j)] [x.sub.j] ln([x.sub.j]), (1)

here S - entropy matrix, N - number of criteria, [x.sub.j] - criteria value, j - criteria change limits (j = 1 ... n).

This method was applied for deciding construction issues (Zavadskas 1987) also in other fields (Liu and Zhang 2011; Mamtani et al. 2006; Li 2009; Ye 2010; Taheriyoun et al. 2010; Hsieh et al. 2010). The algorithm block diagram for entropy method is presented on Figure 1.

[FIGURE 1 OMITTED]

In this case the importance of indices is determined. Their importance demonstrantes what criteria are the most important in comprising with other criteria. For determining criteria importance, the indices are transformed in such a manner that maximum value of each criteria would be the best. While preparing initial data for multi-criteria evaluation by the alternative decision, first of all the list of criteria is made out. These criteria have an impact on the results of the most effective decision. Further in the article the following criteria will be analyzed:

* Growth rate of GDP volume

* Volume indices of production in all building and construction growth rates

* Index of building permits--number of dwellings, new residential buildings

* Index of production, civil engineering, growth rates

* Index of construction costs, new residential buildings

* Total Employment in construction sector

Initial criteria for evaluation of 23 European countries and data are presented in the Table 1.

The values of analyzing criteria for each country are transformed by formula (2), thus the initial matrix without negative values are obtained:

[x.sub.ij] = 100 + [x.sub.ij] */100, (2)

here [x*.sub.ij]--criteria values with negative values, [x.sub.ij]--criteria values without negative values

Data obtained by formula (2) are given in the Table 2.

Further the normalization of the initial matrix (table 2) was performed applying formula (3) and (4):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

The every element of decision matrix is divisible by sum of components from the column where it is located. Thus obtained matrix [P.sub.1].

While transferring decision matrix the indices are determined by formula (5):

[P.sub.ij] = [x.sub.ij]/[m.summation over (i=1)][x.sub.ij], ([for all]ij,i = [bar.1,m]; j = [bar.1,n]), (5)

here [p.sub.ij]-matrix indices, [x.sub.ij]-criteria values.

Criteria obtained by formula (2) are divisible by criteria sum of each column and the final criteria matrix is obtained [bar.P].

The determination of entropy level for each criteria [E.sub.j]:

Ej = -k[m.summation over (i=1)] [p.sub.ij] ln [p.sub.ij], (i = [bar.1, m]; j = [bar.1, n]), (6)

here k = 1:ln m.

As is known, entropy index varies [1,0] by interval, so

0 [is less than or equal to] [E.sub.j] [is less than or equal to] 1, (j = [bar.1,n]), (7)

j-index change level in current tasks is determined:

[d.sub.j] = 1 - [E.sub.j], (j = [bar.1,n]). (8)

If all criteria are equally important i.e. there are no subjective or expert evaluations of their values, criteria importance is determined by formula:

[q.sub.ij] = [d.sub.j]/[n.summation over (j=1)][d.sub.j], (j = [bar.1,n]), (9)

After determination of criteria importance the priority order for considered criteria can be specified:

1. Volume indices of production in all building and construction growth rates.

2. Index of building permits--number of dwellings, new residential buildings..

3. Total Employment in construction sector.

4. Index of production, civil engineering.

5. Index of construction costs, new residential buildings.

6. Growth rate of GDP volume.

In order to evaluate the priority of each European country according to these criteria, COPRAS method is applied.

3. The determination of priority and importance of considered alternatives by COPRAS method

In 1996 COPRAS (Complex Proportional Assessment) method was created (Zavadskas and Kaklauskas 1996). In Lithuania this method is applied in construction, economy, immovable property and management. Zavadskas et al. (2010) evaluates the risks in construction projects in one of articles. The evaluation is based on different multipurpose evaluation methods. Risks evaluation indices are selected taking into account interests, purposes and factors of countries which affect on the construction process efficiency and immovable property price increase. For describing and considering task model, TOPSIS grey and COPRAS-G methods are applied. In another article, using COPRAS, Zavadskas et al. (2009a) carried out the comparative analysis of the fifteen housing enterprises according to 44 criteria taking into account needs of building owners. Kaklauskas et al. (2006) performed significant investigation for Vilnius Gediminas Technical University in order to find the best contractors for the window replacement in the central building. The contractors the best corresponding with the needs of the University were selected from many criteria (heat conductivity, light transmission, lifetime, sound conductivity etc.). Also Kaklauskas et al. (2010b) performed complex analysis of Intelligent Built Environment and evaluated more than 50 criteria of described alternatives for which analysis and reception of results was used COPRAS method. The significant investigations in immovable property were performed by Kanapeckiene et al. (2010), Sliogeriene et al. (2009), Tupenaite et al. (2010) using COPRAS method.

Chatterjee et al. (2011), Karbassi et al. (2008), Mazumdar et al. (2010), Hofer (2009) carried out interesting investigations and made conclusions applying COPRAS method. In the article applying multipurpose evaluation, Chatterjee et al. (2011) studied the efficiency of selection of production materials using three methods: COPRAS, multicriteria decision-making (MCDA) and evaluation of mixed data (EVAMIX) and made the conclusions that COPRAS method is the most efficient and precise. Karbassi et al. (2008) used COPRAS method for investigations of energy efficiency of the building and provision of energy efficiency.

Under varied economic conditions, continuously increasing uncertainties for variety and size, at existence of competitive interactions and risks, it is more difficult to make decisions among set of alternatives therefore these multipurpose evaluation methods are very important and significant under current conditions. According to Zavadskas et al. (2009b), the objective function is directly-proportional depends on indices characterized their alternative of values and weight of those indices. The multipurpose analysis is appropriate for decisions on economy, management, structural and other tasks. In COPRAS method the alternatives are described by values of discrete indices.

In the table 5 the calculation results obtained by COPRAS method are given. Applying COPRAS method, the priority and importance of considered alternatives are calculated at four stages:

1 stage. The normed matrix D is formed. The purpose of this stage is to obtain from comparable indices nondimensional (normalized) evaluation values. If nondimensional evaluation values are known, it may compare the all indices of different units of measurement. This formula is applied:

[d.sub.ij] = [x.sub.ij][q.sub.ij]/[n.summation over (j=1)][x.sub.ij], (i = [bar.1,m]; j = [bar.1,n]), (10)

here [x.sub.ji]--criteria value j decision variant, m-number of criteria, n-number of comparative variants, [q.sub.i]-i criteria importance.

The sum of obtained nondimensional evaluation values [d.sub.ij] for each criteria [x.sub.i] is always equal to the importance of this criteria [q.sub.i]:

[q.sub.i] = [n.summation over (j=1)][d.sub.ij], (i = [bar.1,m]; j = [bar.1,n]). (11)

2 stage. The sum of evaluated normalized minimizing [S.sub.-j] and maximizing [S.sub.+j] values characterized variant j is calculated. The calculations are performed by formula:

[S.sub.+j] = [m.summation over (j=1)][d.sub.+ij]; [S.sub.-j] = [m.summation over (j=1)][d.sub.-ij], (i = [bar.1,m]; j = [bar.1,n]). (12)

3 stage. The relative importance of comparative variants is determined by their characterized positive [S.sub.+j] and negative [S.sub.-j] features. The relative importance of each project [Q.sub.j] is determined using the formula:

[Q.sub.j] = [S.sub.+j] + [S.sub.-min] [n.summation over (j=1)][S.sub.-j]/[S.sub.-j] [n.summation over (j=1)] [S.sub.- min]/[S.sub.- j], (j = [bar.1,n]). (13)

4 stage. The determination of the priority. The more [Q.sub.j], the more efficiency of the country in the construction sector.

On the basis of results obtained in the Table 5 it can conclude that according to selected criteria reflected the situation in construction sector in 2009 and their importance, most efficiently the construction sector market wilts in the countries which hold the first position according to the priority, i.e. in Germany, Austria, Czech Republic, Finland, France, Sweden and Poland. Meanwhile Netherlands, Bulgaria, Lithuania, Estonia, Latvia, Denmark and Slovenia remain short of their most of all.

The data given in the table of final results (5) shows that Lithuania holds position 21 and it is one of the countries which during the construction sector crisis experienced losses and difficulties. The construction activity weight in economic added value structure in 2009 reflects also this fact. The construction activity decreased in 2009 until the level in 2002 and reduced almost by 4 percent than in 2007-2009. Number of employees in construction sector in 2009 in comparison with 2008 reduced by 38 percent. The statistical indices of material investments also confirm the construction sector stagnation. In 2008-2009 investments in production means decreased by one fifth and in immovable property by 40 percent. The similar situation in construction market is in Latvia and Estonia. The decrease of external demand has a high impact on construction sector of the Baltic States; particularly the internal demand wilted which aggravate changes, higher unemployment rate, salary cut and credit crisis (Ozols 2009).

In the international practice the different methods and models for analysis, forecasting, simulation and management of the crisis in construction and immovable property sectors are applied. In order to overcome the economic crisis, the governments of all member states take various measures, including the political, for stimulation the construction activity, particularly for increase of work programs by the state order and speedup of the implementation of planned investments. The heavy expenses for the infrastructure, for example, for roads and railways and nonresidential building construction, maintenance and repair. Some governments introduce tax concessions for demand in specific construction sector parts, particularly housing. Sometimes such measurements are supplemented by the subsidies for renovation and construction, including public building, road and bridge construction projects. Other countries, particularly in Southern Europe, for the purpose of increase of company liquidity partly changed the rules applied for works by the state order, reducing the time from submission of the accounts until their payment. For considering the cyclicality of construction sector and crisis management methods, this sector should be considered in all aspects taken in to account the impact of external and internal environment on it.

4. Conclusions

The progress of national economy and society is impossible without construction sector because construction products for various purposes is necessary for people life, work and satisfaction of social cultural and other requirements. Performed analysis of the literature confirms that there are two main opinions on levels of study of construction sector market: macro economic and micro economic. During the crisis the needs in study and investigations of construction and economic branches are particularly increased; lot of scientists use various methods for analysis, evaluation, forecasting.

In the article six criteria reflected construction sector and 23 European countries are selected according to available statistical data priority. The indices of 2009 reflected percent difference in comprising with 2008 were used for study. The period was selected nonrandom. In the article it was intended to present the countries which most harm due to crisis and countries which develop construction activity well.

Multipurpose evaluation method COPRAS allows sufficiently accurately performing math calculations and evaluate the priority of criteria. For provision data accuracy obtained by entropy method the criteria for weight are determined while evaluating values of minimizing and maximizing indices. After combining entropy and COPRAS methods as well as appropriately performing calculations, the useful information are obtained for further investigations and study.

Obtained results shows that following first five countries develop construction sector most efficiently: Germany, Austria, Czech Republic, Finland, France, and the worst countries: Netherlands, Bulgaria, Lithuania, Estonia, Latvia.

The investigations of European countries are important in the further for checking other periods and analyzing and comprising changes in specific countries as for achievement of efficient management of construction sector it is necessary to study experience of other countries and use practice of other countries.

doi: 10.3846/16111699.2011.575190

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Simona Kildiene (1), Arturas Kaklauskas (2), Edmundas Kazimieras Zavadskas (3)

Vilnius Gediminas Technical University, Faculty of Civil Engineering, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

E-mails: (1) simona.kildiene@vgtu.lt; (2) arturas.kaklauskas@vgtu.lt; (3) edmundas.zavadskas@vgtu.lt

Received 13 July 2010; accepted 26 February 2011

Simona KILDIENE. PhD student of Department of Construction Technology and Management at Vilnius Gediminas Technical University, Vilnius, Lithuania. Master of Science (construction engineering), VGTU, 2010. Bachelor of Science (construction management), VGTU, 2008. Research interests: construction economic, construction management, multiple criteria analysis and decision making theories.

Arturas KAKLAUSKAS. Prof PhD DrSc. Chair in Construction Economics and Real Estate Management Department and Vice-director of the Institute of Internet and Intelligent Technologies at the Vilnius Gediminas Technical University. Lithuanian Science Prize Laureate, Expert member of Lithuanian Academy of Sciences, Leader of the CIB Study group SG1 "The Application of Internet Technologies in Building Economics" and past Advisor of the e-Business Watch Web for ICT and Electronic Business in the Construction Industry. Editor of "International Journal of Strategic Property Management, "Journal of Civil Engineering and Management" and editor of "Facilities" for Central and Eastern Europe. He participated in 9 Framework 5 and 6 projects and author of 221 research publications and 7 monographs.

Edmundas Kazimieras ZAVADSKAS is Principal Vice-Rector of Vilnius Gediminas Technical University, and Head of the Dept of Construction Technology and Management at Vilnius Gediminas Technical University, Vilnius, Lithuania. He has a PhD in Building Structures (1973) and Dr Sc. (1987) in Building Technology and Management. He is a member of the Lithuanian and several foreign Academies of Sciences. He is Doctore Honoris Causa at Poznan, Saint-Petersburg, and Kiev. He is a member of international organisations and has been a member of steering and programme committees at many international conferences. E. K. Zavadskas is a member of editorial boards of several research journals. He is author and co author of more than 400 papers and a number of monographs in Lithuanian, English, German and Russian. Research interests are: building technology and management, decision making theory, automation in design and decision-support systems.

Table 1. Criteria for evaluation of European states and statistic data

No.   Country        Growth         Volume            Index of
                     rate of        indexes of        building per-
                     GDP            production        mits--num-
                     volume-        in all build-     ber of dwell-
                     percent-       ing and           ings, new
                     age            construc-         residential
                     change         tion growth       buildings
                     on previ-      rates com-        (excl. resi-
                     ous year       pared with        dencies for
                     (%)'           previous          communi-
                                    period (%)        ties), growth
                                                      rates (%)

                     max            max               max

1     Austria        -3.9           -1.8              -9.3
2     Belgium        -2.8           -11               -13.2
3     Bulgaria       -4.9           -70.3             -59.3
4     Cyprus         -1.7           -12.7             -17.1
5     Czech          -4.1           -0.5              -17.2
      Republic
6     Denmark        -5.2           -17.5             -51.7
7     Estonia        -13.9          -35.6             -61.8
8     Finland        -8.2           -16.2             -1.5
9     France         -2.6           -6.0              -18.5
10    Germany        -4.7           0.1               3.0
11    Ireland        -7.6           -22.9             -40.1
12    Lithuania      -14.7          -75.3             -52.6
13    Netherlands    -3.9           -6.7              -16.7
14    Portugal       -2.5           -5.9              -42.6
15    Romania        -7.1           -30               -20.1
16    Spain          -3.7           -9.2              -51.0
17    Sweden         -5.3           -4.2              -11.1
18    Slovenia       -8.1           -33.1             -29.7
19    United         -4.9           -11.9             -24.0
      Kingdom
20    Greece         -2.3           -16.1             -25.5
21    Latvia         -18.0          -43.7             -40.2
22    Hungary        -6.7           -3.5              -34.0
23    Poland         1.7            6.6               -23.6

No.   Index of          Index             Total Em-
      produc-           of con-           ployment
      tion, civil       struction         in con-
      engineer-         costs, new        struction
      ing,              residential       sector,
      growth            buildings,        per cent
      rates com-        gross,            variation
      pared with        price             on previ-
      previous          changes           ous year
      period (%)        (%)               (%)

      max               min               max

1     -3.1              0.6               -1.1
2     -3.9              -1.1              -0.8
3     -2.3              10.9              -3.1
4     9.0               0.8               -4.7
5     -2.9              -0.3              -7.6

6     -8.2              -0.4              -13.1
7     3.5               -8.5              -6.0
8     -8.3              -1.1              -5.7
9     -0.1              0.4               -2.0
10    -3.3              0.1               0.3
11    -6.7              -9.9              -26.1
12    -19.9             -14.5             -21.8
13    0.4               0.3               -1.9
14    -5.0              -0.7              -8.8
15    11.9              1.5               -9.0
16    2.5               1.0               -24.9
17    -1.7              2.0               -4.2
18    -5.9              -2.8              -2.3
19    13.6              -7.5              -12.2

20    -12.7             -0.3              -2.6
21    -0.5              -6.2              -3.6
22    -6.0              3.0               -19.1
23    -1.2              0.2               3.6

Table 2. The initial matrix without negative values P

No.    Country        Growth         Volume         Index of
                      rate of        indicies       building
                      GDP            of produc-     permits-
                      volume-        tion in all    number
                      percent-       building       of dwell-
                      age            and con-       ings, new
                      change         struction      residential
                      on previ-      growth         buildings
                      ous year       rates com-     (excl. resi-
                                     pared with     dencies for
                                     previous       communi-
                                     period (%)     ties), growth
                                                    rates (%)
                      max            max            max

1      Austria        0.961          0.982          0.907
2      Belgium        0.972          0.89           0.868
3      Bulgaria       0.951          0.297          0.407
4      Cyprus         0.983          0.873          0.829
5      Czech          0.959          0.995          0.828
       Republic
6      Denmark        0.948          0.825          0.483
7      Estonia        0.861          0.644          0.382
8      Finland        0.918          0.838          0.985
9      France         0.974          0.94           0.815
10     Germany        0.953          1.001          1.03
11     Ireland        0.924          0.771          0.599
12     Lithuania      0.853          0.247          0.474
13     Netherlands    0.961          0.933          0.833
14     Portugal       0.975          0.941          0.574
15     Romania        0.929          0.7            0.799
16     Spain          0.963          0.908          0.49
17     Sweden         0.947          0.958          0.889
18     Slovenia       0.919          0.669          0.703
19     United         0.951          0.881          0.76
       Kingdom
20     Greece         0.977          0.839          0.745
21     Latvia         0.82           0.563          0.598
22     Hungary        0.933          0.965          0.66
23     Poland         1.017          1.066          0.764

No.    Index of       Index          Total Em-
       production,    of con-        ployment
       civil en-      struction      in cons-
       gineering,     costs, new     truction
       seasonally     residential    sector,
       adjusted,      buildings,     per cent
       growth         gross,         variation
       rates com-     price          on previous
       pared with     changes        year
       previous       (%)
       period (%)

       max            min            max

1      0.969          1.006          0.989
2      0.961          0.989          0.992
3      0.977          1.109          0.969
4      1.09           1.008          0.953
5      0.971          0.997          0.924

6      0.918          0.996          0.869
7      1.035          0.915          0.94
8      0.917          0.989          0.943
9      0.999          1.004          0.98
10     0.967          1.001          1.003
11     0.933          0.901          0.739
12     0.801          0.855          0.782
13     1.004          1.003          0.981
14     0.95           0.993          0.912
15     1.119          1.015          0.91
16     1.025          1.01           0.751
17     0.983          1.02           0.959
18     0.941          0.972          0.977
19     1.136          0.925          0.878

20     0.873          0.997          0.974
21     0.995          0.938          0.964
22     0.94           1.03           0.809
23     0.988          0.988          1.039

Table 3. The initial matrix without negative values [P.sub.1]

No.   Country        Growth          Volume          Index of
                     rate of         indicies        building
                     GDP             of produc-      permits-
                     volume-         tion in all     number
                     percentage      building        of dwell-
                     change          and con-        ings, new
                     on previ-       struction       residential
                     ous year        growth          buildings
                                     rates com-      (excl. resi-
                                     pared with      dencies for
                                     previous        communi-
                                     period (%)      ties), growth
                                                     rates (%)

                     max             max             max

1     2              3               4               5
1     Austria        0.944           0.921           0.881
2     Belgium        0.956           0.835           0.843
3     Bulgaria       0.935           0.279           0.395
4     Cyprus         0.967           0.819           0.805
5     Czech          0.943           0.933           0.804
      Republic
6     Denmark        0.932           0.774           0.469
7     Estonia        0.847           0.604           0.371
8     Finland        0.902           0.786           0.956
9     France         0.958           0.882           0.791
10    Germany        0.937           0.939           1.000
11    Ireland        0.909           0.723           0.582
12    Lithuania      0.839           0.232           0.46
13    Netherlands    0.945           0.875           0.809
14    Portugal       0.959           0.883           0.557
15    Romania        0.914           0.657           0.776
16    Spain          0.947           0.852           0.476
17    Sweden         0.931           0.899           0.806
18    Slovenia       0.904           0.628           0.683
19    United         0.935           0.827           0.738
      Kingdom
20    Greece         0.961           0.787           0.723
21    Latvia         0.806           0.528           0.581
22    Hungary        0.917           0.905           0.641
23    Poland         1.000           1.000           0.742

No.   Index of        Index           Total
      production,     of con-         Employment in
      civil en-       struction       construction
      gineering,      costs, new      sector, per
      seasonally      residential     cent
      adjusted,       buildings,      variation on
      growth          gross,          previous
      rates com-      price           year
      pared with      changes
      previous        (%)
      period (%)

      max             min             max

1     6               7               8
1     0.853           0.850           0.955
2     0.846           0.865           0.958
3     0.860           0.771           0.935
4     0.960           0.848           0.920
5     0.855           0.858           0.892

6     0.808           0.858           0.839
7     0.911           0.934           0.907
8     0.807           0.865           0.910
9     0.979           0.852           0.946
10    0.851           0.854           0.968
11    0.821           0.949           0.713
12    0.715           1.000           0.755
13    0.884           0.852           0.947
14    0.836           0.861           0.880
15    0.985           0.842           0.788
16    0.902           0.843           0.725
17    0.865           0.838           0.923
18    0.828           0.880           0.931
19    1.000           0.924           0.848

20    0.768           0.858           0.94
21    0.876           0.912           0.931
22    0.828           0.830           0.781
23    0.870           0.853           1.000

Table 4. Decision matrix [bar.P]

No.   Country        Growth          Volume          Index of
                     rate of         indicies        building
                     GDP             of produc-      permits-
                     volume-         tion in all     number
                     percent-        building        of dwell-
                     age             and con-        ings, new
                     change          struction       residential
                     on previ-       growth          buildings
                     ous year        rates com-      (excl. resi-
                                     pared with      dencies for
                                     previous        communi-
                                     period (%)      ties), growth
                                                     rates (%)

                     max             max             max

1     2              3               4               5
1     Austria        0.044           0.052           0.055
2     Belgium        0.049           0.048           0.053
3     Bulgaria       0.044           0.016           0.025
4     Cyprus         0.045           0.047           0.051
5     Czech          0.044           0.053           0.05
      Republic
6     Denmark        0.044           0.044           0.029
7     Estonia        0.040           0.034           0.023
8     Finland        0.042           0.045           0.06
9     France         0.045           0.05            0.05
10    Germany        0.044           0.054           0.063
11    Ireland        0.043           0.041           0.037
12    Lithuania      0.039           0.043           0.029
13    Netherlands    0.044           0.05            0.051
14    Portugal       0.045           0.05            0.035
15    Romania        0.043           0.037           0.049
16    Spain          0.045           0.049           0.03
17    Sweden         0.044           0.051           0.054
18    Slovenia       0.042           0.036           0.043
19    United         0.044           0.047           0.046
      Kingdom
20    Greece         0.045           0.045           0.045
21    Latvia         0.038           0.03            0.036
22    Hungary        0.043           0.052           0.042
23    Poland         0.047           0.057           0.044

No.   Index of        Index           Total Em-
      production,     of con-         ployment
      civil en-       struction       in cons-
      gineering,      costs, new      truction
      seasonally      residential     sector,
      adjusted,       buildings,      per cent
      growth          gross,          variation
      rates com-      price           on previous
      pared with      changes         year
      previous        (%)
      period (%)

      max             min             max

1     6               7               8
1     0.041           0.043           0.047
2     0.046           0.043           0.047
3     0.041           0.039           0.046
4     0.044           0.042           0.045
5     0.043           0.043           0.044

6     0.041           0.043           0.041
7     0.046           0.047           0.044
8     0.041           0.043           0.044
9     0.044           0.043           0.046
10    0.043           0.043           0.047
11    0.042           0.047           0.035
12    0.036           0.05            0.037
13    0.045           0.043           0.046
14    0.042           0.043           0.043
15    0.05            0.042           0.043
16    0.046           0.042           0.035
17    0.044           0.042           0.045
18    0.042           0.044           0.046
19    0.051           0.046           0.041

20    0.039           0.043           0.046
21    0.044           0.046           0.045
22    0.042           0.042           0.038
23    0.044           0.043           0.048

Table 5. Entropy level, j index change level and criteria importance

Criteria     Growth          Volume          Index of
             rate of         indicies of     building per-
             GDP             production      mits--num-
             volume-         in all build-   ber of dwell-
             percent-        ing and         ings, new
             age             construc-       residential
             change          tion growth     buildings
             on previ-       rates com-      (excl. resi-
             ous year        pared with      dencies for
                             previous        communi-
                             period (%)      ties), growth
                                             rates (%)
             max             max             max

[E.sub.j]    0.99987         0.98774         0.98964
[d.sub.j]    0.00013         0.01226         0.01036
[q.sub.j]    0.0053          0.4975          0.4205

Criteria     Index of        Index           Total Em-
             produc-         of con-         ployment
             tion, civil     struction       in cons-
             engineering,    costs, new      truction
             seasonally      residential     sector,
             adjusted,       buildings,      per cent
             growth          gross, price    variation
             rates com-      changes         on previous
             pared with      (%)             year
             previous
             period (%)

             max             min             max

[E.sub.j]    0.99935         0.99979         0.99897
[d.sub.j]    0.00065         0.00021         0.00103
[q.sub.j]    0.0264          0.0085          0.0418

Table 6. Quantitative information characterized construction sector of
twenty European countries

Quantitative information characterized construction sector of twenty
European countries

                            Significance    Measures
Considered criteria    *

Growth rate of GDP     +       0.0053           %
volume--percentage
change on previous
year

Volume indices of      +       0.4996           %
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building      +       0.4188           %
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,   +       0.0263           %
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of               -       0.0085           %
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in    +       0.0416           %
construction sector,
per cent variation
on previous year

Sum of evaluated
normalized
maximizing values

Sum of evaluated
normalized
minimizing values

Importance of
alternative

Priority of country

                       Considered countries

Considered criteria     Austria     Belgium    Bulgaria     Cyprus

Growth rate of GDP      0.0009      0.0009      0.0011      0.0009
volume--percentage
change on previous
year

Volume indices of        0.084      0.0781      0.0341      0.0757
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building       0.0656      0.0644      0.0363      0.0608
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,    0.0044      0.0045      0.0055       0.005
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                0.0015      0.0015       0.002      0.0015
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in     0.0071      0.0073      0.0086      0.0069
construction sector,
per cent variation
on previous year

Sum of evaluated        0.1620      0.1551      0.0829      0.1494
normalized
maximizing values

Sum of evaluated        0.0015      0.0015       0.002      0.0015
normalized
minimizing values

Importance of           0.1633      0.1564      0.0838      0.1507
alternative

Priority of country        2           8          22          11

                       Considered countries

Considered criteria      Czech      Denmark     Estonia     Finland
                       Republic

Growth rate of GDP      0.0009       0.001       0.001      0.0009
volume--percentage
change on previous
year

Volume indices of       0.0872      0.0815      0.0671      0.0746
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building       0.0614      0.0403      0.0336      0.0741
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,    0.0045      0.0048      0.0057      0.0043
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                0.0015      0.0017      0.0016      0.0015
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in     0.0068      0.0072      0.0082      0.0071
construction sector,
per cent variation
on previous year

Sum of evaluated        0.1608      0.1348      0.1156      0.1609
normalized
maximizing values

Sum of evaluated        0.0015      0.0017      0.0016      0.0015
normalized
minimizing values

Importance of           0.1627      0.1359      0.1168      0.1622
alternative

Priority of country        3          18          20           4

                       Considered countries

Considered criteria     France      Germany     Ireland    Lithuania

Growth rate of GDP      0.0007      0.0008       0.001       0.0011
volume--percentage
change on previous
year

Volume indices of       0.0854      0.0836      0.0788       0.0306
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building       0.0626      0.0727      0.0518       0.0497
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,    0.0048      0.0043      0.0051       0.0053
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                0.0016      0.0014      0.0016       0.0018
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in     0.0075       0.007      0.0063       0.0081
construction sector,
per cent variation
on previous year

Sum of evaluated        0.1609      0.1685      0.1430       0.0949
normalized
maximizing values

Sum of evaluated        0.0016      0.0014      0.0016       0.0018
normalized
minimizing values

Importance of           0.1622      0.1699      0.1442       0.0959
alternative

Priority of country        5           1          14           21

                       Considered countries

Considered criteria    Netherlands    Portugal     Romania      Spain

Growth rate of GDP        0.0001        0.001      0.0009       0.001
volume--percentage
change on previous
year

Volume indices of         0.0137       0.0876      0.0628      0.0878
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building         0.0106       0.0452      0.0606       0. 0
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,      0.0008       0.0047      0.0057      0.0053
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                  0.0003       0.0016      0.0016      0.0017
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in       0.0012       0.0071      0.0069      0.0061
construction sector,
per cent variation
on previous year

Sum of evaluated          0.0264       0.1455      0.1369      0.1401
normalized
maximizing values

Sum of evaluated          0.0003       0.0016      0.0016      0.0017
normalized
minimizing values

Importance of             0.0341       0.1468      0.1381      0.1413
alternative

Priority of country         23           13          16          15

                       Considered countries

Considered criteria     Sweden     Slovenia     United      Greece
                                                Kingdom

Growth rate of GDP      0.0009      0.0009      0.0009       0.001
volume--percentage
change on previous
year

Volume indices of       0.0828      0.0642      0.0792      0.0772
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building       0.0649      0.0571      0.0578       0.058
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,    0.0045      0.0048      0.0054      0.0043
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                0.0015      0.0016      0.0014      0.0016
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in      0.007      0.0079      0.0066      0.0075
construction sector,
per cent variation
on previous year

Sum of evaluated        0.1601      0.1349       0. 5       0.1479
normalized
maximizing values

Sum of evaluated        0.0015      0.0016      0.0014      0.0016
normalized
minimizing values

Importance of           0.1614      0.1361      0.1514      0.1492
alternative

Priority of country        6          17          10          12

                       Considered countries

Considered criteria     Latvia      Hungary     Poland

Growth rate of GDP      0.0009      0.0009      0.0009
volume--percentage
change on previous
year

Volume indices of       0.0574       0. 0       0.0905
production in all
building and
construction growth
rates compared with
previous period (%)

Index of building       0.0515       0.052      0.0548
permits--number of
dwellings, new
residential
buildings (excl.
residencies for
communities), growth
rates (%)

Index of production,    0.0054      0.0046      0.0045
civil engineering,
seasonally adjusted,
growth rates
compared with
previous period (%)

Index of                0.0016      0.0016      0.0014
construction costs,
new residential
buildings, gross,
price changes (%)

Total Employment in     0.0083      0.0063      0.0074
construction sector,
per cent variation
on previous year

Sum of evaluated        0.1235      0.1539      0.1581
normalized
maximizing values

Sum of evaluated        0.0016      0.0016      0.0014
normalized
minimizing values

Importance of           0.1247      0.1551      0.1595
alternative

Priority of country       19           9           7