ABSTRACT. This paper considers the application of methodology for
the defining the utility and market value of a real estate. The
theoretical basis of the methodology is developed. The proposed methods,
the method of multiple criteria complex proportional assessment (COPRAS)
and the method of defining the utility and market value of a real estate
assume the dependence of priority, utility degree and value of
investigated versions on a system of criteria adequately describing the
alternatives and their direct proportionality to the values and weights
of these criteria. The procedure of the defining the utility and market
value of a real estate is discussed using an example.
KEYWORDS: Multiple criteria analysis; Utility and market value;
Real estate
1. INTRODUCTION
Many decision making models and methods have been developed in the
world for solving different problems in real estate sector. Kuo (1996)
proposed a method of polynomial approximation to value the housing price
dynamics and the valuation of mortgage default options. Gonzalez and
Laureano-Ortiz (1992) concentrated on the issues involved in the
application of the case-based reasoning techniques to a specific domain,
property appraisal. Case-based reasoning has been recently favored
because it seems to resemble more closely the psychological process
humans follow when trying to apply their knowledge to the solution of
problems: adapting solutions of similar problems handled in past
experiences to address present situations. By modelling the market data
approach of appraisal, using adaptations of case-based reasoning
techniques, such as the similarity links and the critics, and
integrating other techniques, (i.e., the use of comfort factors), a
case-based reasoner for property appraisal is implemented addressing the
issues just mentioned above (Gonzalez and Laureano-Ortiz, 1992).
Diappi and Bolchi (2007) investigated local housing market dynamics
by applying an urban spatial model of gentrification based on
Smith's rent gap theory. Smith's supply side approach explains
the emergence of gentrifying neighbourhoods on the basis of investments
spent in "large scale renewal projects" which only investors
or developers looking for profits are able to carry out. They invest in
degraded areas on the base of the gap between the actual rent and the
potential rent after rehabilitation (rent gap). A set of factors are
selected and a statistical early-warning method, which can monitor the
Shenzhen real estate property market, is developed by Huang and Wang
(2005). In addition, a system dynamics model has been developed, which
can provide a simulation tool to predict the effect of regulatory
policies on the real estate market. Evaluation results indicate that the
pre-warning system can provide useful information to regulate the
property market in Shenzhen.
Markland (1979) described a Monte Carlo simulation approach to the
analysis of real estate investments under uncertainty. Wang (2005)
described a knowledge-based decision support system for measuring the
performance of government real estate investment using DEA models.
Trippi (1989) examined industry factors, design goals, and functions of
a system used to improve major real property asset acquisition,
improvement, and divestment decisions. Fletcher et al. (2000) were
concerned as to whether it is more appropriate to use aggregate or
disaggregate models in forecasting house prices when using hedonic
modeling. Baffoe-Bonnie (1998) analyzed the dynamic effects of four key
macroeconomic variables on housing prices and the stock of houses sold
at national and regional levels by using a nonstructural estimation
technique. Hui and Yu (2006) analyzed the dynamics of Hong Kong's
office rental market. This study provides a generator approach, on the
basis of both system dynamics and econometric modeling. Dua et al.
(1999) used Bayesian vector autoregressive models to examine the
usefulness of leading indicators in predicting U.S. home sales. Wheaton
et al. (1997) applied structural econometric methodology for estimating
and forecasting the greater London office market. Magdisyuk (2001)
considered some aspects of using a cascade-correlation network in the
investment task, in which it is required to determine the most suitable
project to invest money. Leung and Hui (2000) attempted to introduce the
application of the option pricing theory to the valuation of property
development projects by integrating both the capital budgeting and the
strategic planning that were based on the London Docklands saga.
Lins et al. (2005) proposes a new methodology for the assessment of
the value range for real estate units. The proposed approach-christened
Double Perspective-Data Envelopment Analysis (DP-DEA)--is applied to a
database comprising the prices and features of the units under
assessment. It is shown that the DP-DEA presents some specific
advantages when compared to the usual regression analysis method
employed in real estate value assessment. Englund et al. (1998)
presented an improved methodology for estimating asset prices for real
estate and other durables. The method is used to analyze house price
dynamics by exploiting an unusually rich and detailed body of
data-extensive descriptive and financial information on every house sale
in Sweden during a 12-year period.
Cannaday et al. (2005) developed a multivariate repeat-sales model
that is able to separately control for the effects of age and time, as
well as other assets with changing attributes in the construction of
price indices. Martinaitis et al. (2007) proposed a two-factor method
for appraising building renovation and energy efficiency improvement
projects. Ioannides (2003) examined effects of social interactions in
the form of reaction functions for homeowners' valuation of their
properties at the level of the immediate residential neighborhood, with
neighborhoods consisting of a randomly chosen dwelling unit and about
ten nearest neighbors. The paper provides empirical support for the
notion, common in the real estate world, of the importance of
neighboring properties in property valuations. Gibbons and Machin (2003)
provided the first empirical evidence for the UK on the effect of
primary school performance on property prices. Bourassa et al. (2006)
presented the sale price appraisal ratio (SPAR) method for constructing
house price indexes. Authors compared the official New Zealand indexes
for three urban areas with repeat sales and hedonic indexes created from
the same transactions data, and observed that the SPAR method produced
an index very much like those produced by repeat sales methods.
Mendez (2006) estimated the value of legal property titles on the
Costa Rican urban housing market using hedonic regressions on the value
of the house and then studied specific segments of the population that
vary in their economic activities and incentives as related to legal
housing titles. Arguea and Hsiao (2000) presented a latent variable
framework to provide consistent and efficient estimates of market values
of amenities. They used samples obtained from the American Housing
Survey (AHS) to estimate the effect of neighborhood quality on housing
prices.
However, fewer attempts have been made to employ methods of
multiple criteria decision making (MCDM) to solve a number of problems
in real estate sector (see Zavadskas and Kaklauskas, 1996; Zavadskas et
al., 1997; Maliene et al., 1999; Zavadskas et al., 2001; Zavadskas et
al., 2004a; Zavadskas et al., 2004b; Kaklauskas and Gikys, 2005;
Kaklauskas et al., 2005). In this paper, the authors present a
methodology for the defining the utility and market value of a real
estate. The proposed methods, the method of multiple criteria complex
proportional assessment (COPRAS) and the method of defining the utility
and market value of a real estate assume the dependence of priority,
utility degree and value of investigated versions on a system of
criteria adequately describing the alternatives and their direct
proportionality to the values and weights of these criteria. The
potential of the approach has been explored in Framework 5 (2000),
Framework 5 (2001), Framework 6 (2003) and ACE PHARE programme
(Kaklauskas, 1998), for instance. Real-world applications demonstrate
the effectiveness of this approach in solving wide-range problems (see
Ministry of Construction and Urban Development of the Republic of
Lithuania, 1998; Ministry of Economy of the Republic of Lithuania,
2001). In view of our theoretical and practical results, we believe that
the proposed approach is especially suitable for decision contexts where
multiple dimensions of problems must be evaluated and due attention to
interests of participants involved must be given. The proposed
methodology allows the decision maker to negotiate his/her preferences
and needs.
The remainder of this paper is structured as follows. Section 2
presents the methodology for the determination of the utility degree and
market value of a real estate. An example is given in Section 3 to
illustrate the use of the methodology. Finally, some concluding remarks
are provided in Section 4.
2. A MULTIPLE CRITERIA APPROACH
2.1. Collection of initial data and determination of the criteria
weights
The determination of the utility degree and market value of the
real estate under investigation and the establishment of the order of
priority for its implementation has less difficulty if the criteria
numerical values and weights are obtained and when multiple criteria
decision making methods are used.
The data for the analysis of real estate projects are presented as
a grouped decision matrix that involves a set of n alternatives, to be
compared with respect to a set of m criteria (Table 1). For evaluating
competing alternatives (the real estate to be valued and comparable real
estates), a complex analysis of its economical, technical, qualitative,
infrastructure and other aspects is needed. Quantitative and conceptual
descriptions provide this information. Quantitative information is based
on criteria system, units of measurement, values and weights of the
criteria. The determination of quantitative criteria numerical values is
based on the use of various statistical methods, analysed projects,
recommendations, price-lists, reference books, building codes,
specifications and other documents.
The diversity of aspects being assessed should include a variety of
presented data needed to decide. Therefore, the conceptual information
may be presented in numerical, textual, graphical, and audio/video
format. The conceptual descriptions of criteria and reasons for a choice
of the criteria's system, their values and weights should all be
analyzed. Conceptual information is needed to make more complete and
accurate evaluation of the real estate alternatives considered. It also
helps to get more useful information as well as developing a system and
subsystems of criteria and defining their values and weights.
In order to define the utility degree and market value of a real
estate, it is necessary, to have formed the decision matrix, to perform
multiple criteria analysis. MCDM refers to making preference decisions
on the competing alternatives (the real estate to be valued and
comparable real estates) in terms of multiple criteria. Typically, each
alternative is evaluated on the established set/system of criteria. One
of the major tasks is to determine the weights of the criteria. This is
most often done with the use of experts' assessments.
Having determined the weights of criteria by a panel of experts, we
express our preferences in terms of the relative importance of criteria.
With a change of values of quantitative criteria, their weight changes
as well. The method developed by the authors (Kaklauskas, 1996;
Kaklauskas, 1999) takes into account criteria's quantitative and
qualitative aspects.
2.2. A method of multiple criteria complex proportional assessment
The method of multiple criteria complex proportional assessment
(COPRAS) (Zavadskas and Kaklauskas, 1996), presented here, uses a
stepwise ranking and evaluating procedure of the alternatives in terms
of significance and utility degree.
The procedure of the method of complex proportional evaluation
consists of the following steps:
(1) Calculation of the weighted normalized decision matrix (Table
2). The purpose of this step is to receive dimensionless weighted values
from the comparative indexes. When the dimensionless values of the
indexes are known, all criteria, originally having different dimensions,
can be compared. The weighted normalized value [d.sub.ij] is calculated
as
[d.sub.ij] = [x.sub.ij] - [q.sub.i] / [n.summation over (j = 1)]
[x.sub.ij], i = [bar.1,m]; j = [bar.1, n]. (1)
where: [x.sub.ij] is the value of the i criterion in the j
alternative of a solution; m is the number of criteria; n is the number
of the alternatives compared; [q.sub.i] is weight of i criterion.
The sum of dimensionless weighted index values [d.sub.ij] of each
criterion [x.sub.i] is always equal to the weight [q.sub.i] of this
criterion
[q.sub.i] = [n.summation over (j=1)] [d.sub.ij], i = [bar.1,m]; j =
[bar.1, n]. (2)
In other words, the value of weight [q.sub.i] of the investigated
criterion is proportionally distributed among all alternative versions
[a.sub.j] according to their values [x.sub.ij].
(2) Calculation of the sums of maximizing indexes ([S.sub.+j]) and
minimizing indexes ([S.sub.-j]) describing the real estate. The lower
value of minimizing indexes is better (price of the plot and building,
etc.). The greater value of maximizing indexes is better (comfortability
and aesthetics of the building, etc.). The values [S.sub.+j] and
[S.sub.-j] are calculated as
[S.sub.+j] = [m.summation over (i=1)] [d.sub.+ij]; [S.sub.-j] =
[m.summation over (i=1)] [d.sub.-ij],
i = [bar.1,m]; j = [bar.1, a] (3)
In this case, the values [S.sub.+j] (the greater is this value, the
more satisfied are the interested parties) and [S.sub.-j] (the lower is
this value, the better is goal attainment by the interested parties)
express the degree of goals attained by the interested parties in each
alternative. In any case the sums of 'pluses' [S.sub.+j] and
'minuses' [S.sub.-j] of all alternatives is always
respectively equal to all sums of weights of maximizing and minimizing
criteria
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)
In this way, the calculations made may be additionally checked.
(3) Determination of the significance of the alternative based on
positive and negative characteristics. The relative significance
[Q.sub.j] of each alternative j is defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)
(4) Determination of the priority of the real estate. The greater
significance [Q.sub.j], the higher is the priority (rank) of the real
estate. The relative significance [Q.sub.j] of real estate j indicates
the satisfaction degree of the needs of the interested parties. In the
case of [Q.sub.max], the satisfaction degree is the highest. The
relative significance of other real estate is lower, and the needs of
the interested parties and the real estate are satisfied to a smaller
extent than in the best real estate.
2.3. A method of defining the utility and market value of a real
estate
The degree of real estate utility is directly associated with
quantitative and conceptual information related to it. If one real
estate is characterized by the best comfortability, aesthetics, price
indices, while the other shows better maintenance and facilities
management characteristics, both having obtained the same significance
values as a result of multiple criteria evaluation, this means that
their utility degree is also the same. With the increase (decrease) of
the significance of a real estate analyzed, its degree of utility also
increases (decreases). The degree of real estate utility is determined
by comparing the analyzed real estate with the best real estate. The
values of the utility degree are from 0% to 100% between the worst and
the best real estate alternatives.
The degrees of utility of the real estate considered as well as the
market value of a real estate being valuated are determined in seven
steps:
(1) The utility degree [N.sub.j] of each real estate alternative
[a.sub.j] is calculated as
[N.sub.j] = ([Q.sub.j] : [Q.sub.max]). 100%, (6)
where: [Q.sub.j] and [Q.sub.max] are the significances of the real
estate obtained from the equation 5.
The degree of utility [N.sub.j] of real estate [a.sub.j] indicates
the level of satisfying the needs of the parties interested in the real
estate. The more goals are achieved and the more important they are, the
higher is the degree of the real estate utility. Since clients are
mostly interested in how much more efficient particular real estate are
than the others (which ones can better satisfy their needs), then it is
more advisable to use the concept of real estate utility rather than
significance when choosing the most efficient solution.
A degree of real estate utility reflects the extent to which the
goals pursued by the interested parties are attained. Therefore, it may
be used as a basis for determining real estate market value. The more
objectives are attained and the more significant they are the higher
will be real estate degree of utility and its market value.
Thus, having determined in such a way the ratio of degree of
utility and market value of real estate, one can see what complex effect
can be obtained by investing money into anyone of the real estate. There
is a complete clarity where it pays better to invest the money and what
is the efficiency degree of the investment.
(2) Calculation of the efficiency degree [E.sub.xj] of money
invested into real estate [a.sub.j]. It shows by how many percent it is
better (worse) to invest money into real estate [a.sub.x] compared with
real estate [a.sub.j]. The efficiency degree [E.sub.xj] is calculated as
[E.sub.xj] = [N.sub.x] - [N.sub.j], (7)
(3) Calculation of the mean deviation [k.sub.x] of the utility
degree [N.sub.x] of the real estate [a.sub.x] from the same index of
other real estate (n-1) (Table 3). The mean deviation [k.sub.x] is
calculated as
[k.sub.x] = [n.summation over (j=1)] [E.sub.xj]:(n-1), (8)
(4) The initial value of the real estate being valuated is
calculated as
[x.sub.11] = [n.summation over (j=2)][ [x.sub.1j]: (n-1), (9)
In grouped decision matrix (Table 1), the real estate [a.sub.1] to
be valuated should be assigned the market value ([x.sub.11-R]). Other
comparison standard real estate ([a.sub.2] - [a.sub.n]) were sold, their
purchasing/selling prices ([x.sub.12]-[x.sub.1n]) known. All the values
and weights of the criteria relating to other real estate are also
known.
The problem may be stated as follows: what market value
[x.sub.11-R] of the valuated real estate al will make it equally
competitive on the market with comparison standard real estate
([a.sub.2]-[a.sub.n])? This may be determined if a complex analysis of
the benefits and drawbacks of the real estate is made.
Using a grouped decision matrix (Table 1) and the equations 1-9 the
calculations are made.
(5) The corrected value x11_ of the real estate to be valuated
[a.sub.1] is calculated as
[x.sub.11-p] = [x.sub.11](1 + [k.sub.1]=100, (10)
(6) Determination whether the corrected value x11_R of the real
estate being valuated al had been calculated accurately enough
| [k.sub.1] | < s, (11)
where: s is the accuracy, %, to be achieved in calculating the
market value [x.sub.11-p] of the real estate [a.sub.1].
(7) Determination of the market value [x.sub.11]-of the real estate
al to be valuated. If in- equality 11 is satisfied the market value of
the real estate [a.sub.1] may be found as
[x.sub.1-R] = [x.sub.11-p]. (12)
If inequality 11 is not satisfied this means that the value of the
real estate being valuated had not been calculated accurately enough and
the approximation cycle should be repeated. In this case, the corrected
value [x.sub.11]=[x.sub.11-p] of the real estate being valuated is
substituted into a grouped decision making matrix of real estate
multiple criteria analysis and the calculations according to the
equations 1-10 should be repeated until the inequation 11 is satisfied.
3. ESTIMATION OF THE MARKET VALUE FOR THE SINGLE-FAMILY DWELLING
In the sales comparison approach, market value is estimated by
comparing properties similar to the subject real estate that have
recently been sold, are listed for sale, or are under contract. A major
premise of the sales comparison approach is that the market value of a
real estate is directly related to the prices of comparable, competitive
properties. The value difference between two properties is calculated by
multiplication of the differences in the characteristics considered,
with marginal adjustment factors for those characteristics.
A sample valuation case study is analyzed in order to illustrate
the use of the multiple criteria approach presented above. Two
comparable single-family dwellings were selected for the single-family
dwelling being valued. Both are located in Vilnius. The single-family
dwelling being valued and the comparable single-family dwellings contain
differences in quality, quantity and market conditions. When drawing up
the system of criteria describing the single-family dwelling being
valued and the comparable single-family dwellings, it is worthwhile to
take into account the suggestions of other authors as well. Data for the
determination of the system of criteria and their weights of the
single-family dwelling being valued and the comparable single-family
dwellings were collected by the questionnaires that were mailed to
experts in Lithuania, based on the use of suggestions of experts, as
well as reference books and recommendations. For example, the 35 experts
were asked to prioritize the 28 criteria listed in Table 4. The
respondents were property scientists, real estate appraisers, brokers,
and other specialists. The determination of quantitative criteria values
is based on the use of analyzed projects, pricelists, specifications,
reference books and recommendations. The description of the
single-family dwelling being valued and the comparable single-family
dwellings is presented further on in this paper.
3.1. Description of the single-family dwelling being valued
The single-family dwelling under valuation here, are located on
district Bukciai in Vilnius, 5 kilometers from the city center, next to
the river Neris (0.5 km). 7 ares cover an area of plot situated at Ruko
Street, the ground of which is clay loam. Form of plot is a regular
rectangle; the plot is bounding to neighboring plots from three sides.
The built area of the plot covers 130 [m.sup.2], number of stores--two,
the dwelling house is brick-built with economic heat insulation, but
still under installation, external finishing is completed 60%, two
telephone lines are installed. Modern and up-to-date construction
materials were used. A garage is equipped near the house. The total
floor-space of the building makes up 260 [m.sup.2]. The dwelling house
is in good condition. Engineering lines are municipal.
The initial market value (selling price) of the single-family
dwelling under investigation ([x.sub.11]= 380.00 thousand EURO, 1 EURO
is equal to 3.4528 LTL) was accepted according to the developed maps of
real estate values.
3.2. Description of the first comparable single-family dwelling
The comparable single-family dwelling is located on district
Bukciai in Vilnius, 5 kilometers from the city center, next to the river
Neris (0.5 km). 13 ares cover an area of a plot of land situated at Ruko
Street, the ground of which is clay loam. Form of the plot of land is a
regular rectangle; the plot of land is bounding to neighboring plots of
land from three sides. The built area of the plot of land covers 160 m2.
Two-storey dwelling house is well appointed completely. The dwelling
house was erected in 2004, and it includes as follows: 5 rooms, 2
garages, telephone, wood windows of glass package, framed doors, a
fire-place equipped, heating by solid fuel, gaseous and electric power.
Walls of the building are plastered, puttied and painted, external walls
of the building have thermal insulation, and floors are made of wood.
The total floor-space of the building makes up 280 [m.sup.2]. The
dwelling house is in good condition. First comparable single-family
dwelling was sold for 360.00 thousand EURO.
3.3. Description of the second comparable single-family dwelling
The comparable single-family dwelling is located on district
Bukciai in Vilnius, 5 kilometers from the city center, next to the river
Neris (0.5 km). The plot of land situated at Ruko Street. Area of the
plot of land makes up to 6 ares, the ground of which is sandy loam. Form
of the plot of land is a regular rectangle; it is bounding to
neighboring plots of land from two sides. The plot of land is equipped.
Local sewerage system is available. The built area of the plot of land
covers 120 [m.sup.2]. Two-storey dwelling house with a mansard erected
in 2003, containing 5 rooms, three sanitation premises, ceiling
constructions are made of reinforced concrete, tinplate roof, thermal
insulation, braced, windows of glass packet, parquet floor, puttied and
painted walls. 2 garages are equipped in the house, a greenhouse, and
single telephone line available. The total floor-space of the building
makes up 240 [m.sup.2]. Cellar and the mansard are not equipped. The
dwelling house is in good condition. It is possible to expand the plot
of land at 7 ares by buying up from the state. Second comparable
single-family dwelling was sold for 410.00 thousand EURO.
3.4. Investigation process and summary of results
Regarding the main characteristics of qualitative, quantitative and
market descriptions of the single-family dwelling under valuation and
the comparable single-family dwellings, a grouped decision matrix was
formed (Table 4).
Using a grouped decision making matrix (Table 4) and the equations
1-12 the calculations are made. The results of the multiple criteria
analysis of the single-family dwellings are given in Table 5.
The market value of the single-family dwelling was estimated in 8
cycles of approximation, until the mean deviation [k.sub.x], of the
degree of utility of the single-family dwellings under valuation,
calculated in step 7 of the method, satisfied the condition | [k.sub.1]
| < 1%. As it is seen from the Table 6, the calculated initial
single-family dwelling value [x.sub.11-p] in the first approach was
equated to 380.00 thousand EURO. However in the first approach the
accuracy of | [k.sub.11 | = -17.95% was reached instead of the required
1%. In the remaining seven approach stages the calculation accuracy of
the single-family dwelling value | [k.sub.1 | increased--12.50%,
-7.60%,-4.60%,-2.75%,-1.70%,-1.05%) until it (|[k.sub.18| = |-0.60%|)
not exceeded 1% (Table 6).
4. CONCLUSION
The methodology for the defining the utility and market value of a
real estate developed by authors has been presented in this paper. The
proposed methods, the method of multiple criteria complex proportional
assessment (COPRAS) and the method of defining the utility and market
value of a real estate assume the dependence of priority, utility degree
and value of investigated versions on a system of criteria adequately
describing the alternatives and their direct proportionality to the
values and weights of these criteria. Using this methodology, a
participant/decision maker can evaluate alternatives of the real estate
in terms of criteria both qualitative and quantitative. The approach
allows evaluating the satisfaction degree of the needs of the
participants involved such as buyers, sellers, developers, investors,
etc. and the real estate. A sample valuation case study is presented in
order to illustrate the use of the developed multiple criteria approach.
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Arturas KAKLAUSKAS (1), Edmundas K. ZAVADSKAS (2), Audrius BANAITIS
(1), Gintautas SATKAUSKAS (1)
(1) Department of Construction Economics and Property Management,
Vilnius Gediminas Technical University, Sauktekio al. 11, LT 10223
Vilnius, Lithuania E-mail: Arturas.Kaklauskas@st.vtu.lt (2) Department
of Construction Technology and Management, Vilnius Gediminas Technical
University, Sauletekio al. 11, LT 10223 Vilnius, Lithuania E-mail:
Edmundas.Zavadskas@adm.vtu.lt
SANTRAUKA DAUGIAKRITERINIS NEKILNOJAMOJO TURTO NAUDINGUMO LAIPSNIO
IR VERTES NUSTATYMAS
Arturas KAKLAUSKAS, Edmundas K. ZAVADSKAS, Audrius BANAITIS,
Gintautas SATKAUSKAS
Straipsnyje aprasomas daugiakriterinis nekilnojamojo turto
naudingumo laipsnio ir vertes nustatymas pagal autoritl siulomus
metodus: daugiakriterini kompleksinio proporcingo ivertinimo ir
daugiakriterini naudingumo laipsnio ir vertes nustatymo metoda.
Nagrinejamu nekilnojamojo turto variantu prioritetiskumas ir
reiksmingumas tiesiogiai ir proporcingai priklauso nuo alternatyvas
adekvaciai apibudinanciu kriteriju sistemos, kriteriju reiksmiu ir
reiksmingumu dydziu. Naudingumo laipsnis rodo suinteresuotu grupiu
pasiektu tikslu lygi. Todel juo remiantis nustatoma nekilnojamojo turto
verte. Atsizvelgus i visu analizuojamu nekilnojamojo turto alternatyvu
naudingumo laipsnius, skaiciuojama konkretaus nekilnojamojo turto
(alternatyvos) verte. Remiantis pateiktais metodais, buvo nustatyta
vienbucio gyvenamojo namo rinkos verte.
Received 8 September 2006; accepted 15 December 2006
Table 1. Grouped decision matrix of a multiple criteria analysis of
the real estate to be valued
Criteria * Weights Measuring
units
Quantitative criteria
[X.sub.1] [z.sub.1] [q.sub.1] [m.sub.1]
[X.sub.2] [z.sub.2] [q.sub.2] [m.sub.2]
... ... ... ...
[X.sub.i] [z.sub.i] [q.sub.i] [m.sub.i]
... ... ... ...
[X.sub.t] [z.sub.t] [q.sub.t] [m.sub.t]
Qualitative criteria
[X.sub.t+1] [z.sub.t+1] [q.sub.t+1] [m.sub.t+1]
[X.sub.t+2] [z.sub.t+2] [q.sub.t+2] [m.sub.t+2]
... ... ... ...
[X.sub.m] [z.sub.m] [q.sub.m] [m.sub.m]
Conceptual information pertinent to real estate (texts,
drawings, graphics, tapes)
[C.sub.f] [C.sub.z] [C.sub.q] [C.sub.m]
Real estate to be valued and
Criteria comparable real estates
[a.sub.1] [a.sub.2] ...
Quantitative criteria
[X.sub.1] [x.sub.11] [x.sub.12] ...
[X.sub.2] [x.sub.12] [x.sub.22] ...
... ... ... ...
[X.sub.i] [x.sub.i1] [x.sub.i2] ...
... ... ... ...
[X.sub.t] [x.sub.t1] [x.sub.i2] ...
Qualitative criteria
[X.sub.t+1] [x.sub.t+1] [x.sub.t+1] ...
[X.sub.t+2] [x.sub.t+2] [x.sub.t+2] ...
... ... ... ...
[X.sub.m] [x.sub.m1] [x.sub.m2] ...
Conceptual information pertinent to real estate (texts,
drawings, graphics, tapes)
[C.sub.f] [C.sub.1] [C.sub.2] ...
Real estate to be valued and
Criteria comparable real estates
[a.sub.j] ... [a.sub.n]
Quantitative criteria
[X.sub.1] [x.sub.1j] ... [x.sub.1n]
[X.sub.2] [x.sub.2j] ... [x.sub.2n]
... ... ... ...
[X.sub.i] [x.sub.ij] ... [x.sub.in]
... ... ... ...
[X.sub.t] [x.sub.tj] ... [x.sub.tn]
Qualitative criteria
[X.sub.t+1] [x.sub.t+1] ... [x.sub.t+1]
[X.sub.t+2] [x.sub.t+2] ... [x.sub.t+2]
... ... ... ...
[X.sub.m] [x.sub.mj] ... [x.sub.mn]
Conceptual information pertinent to real estate (texts,
drawings, graphics, tapes)
[C.sub.f] [C.sub.j] ... [C.sub.n]
*--The sign z [sub.i] (+ (-)) indicates that a greater/lesser
criterion value corresponds to a greater weight for a client
Table 2. Multiple criteria analysis of the real estate
Criteria * Weights
[X.sub.1] [z.sub.1] [q.sub.1]
[X.sub.2] [z.sub.2] [q.sub.2]
... ... ...
[X.sub.i] [z.sub.i] [q.sub.i]
... ... ...
[X.sub.t] [z.sub.t] [q.sub.t]
... ... ...
[X.sub.t+1] [z.sub.t+1] [q.sub.t+1]
[X.sub.t+2] [z.sub.t+2] [q.sub.t+2]
... ... ...
[X.sub.i] [z.sub.i] [q.sub.i]
... ... ...
[X.sub.m] [z.sub.m] [q.sub.m]
The sums of weighted
normalized maximizing
indices
The sums of weighted
normalized minimizing
indices
Significance of the
real estate
Real estate's
priorities
Real estate's utility
degree (%)
Criteria Real estate to be valued and
comparable real estates
[a.sub.1] [a.sub.2] ...
[X.sub.1] [d.sub.11] [d.sub.12] ...
[X.sub.2] [d.sub.21] [d.sub.22] ...
... ... ... ...
[X.sub.i] [d.sub.i1] [d.sub.i2] ...
... ... ... ...
[X.sub.t] [d.sub.t1] [d.sub.t2]
... ... ... ...
[X.sub.t+1] [d.sub.t+11] [d.sub.t+12]
[X.sub.t+2] [d.sub.t+21] [d.sub.t+22]
... ... ... ...
[X.sub.i] [d.sub.i1] [d.sub.i2] ...
... ... ... ...
[X.sub.m] [d.sub.m1] [d.sub.m2]
The sums of weighted [S.sub.+1] [S.sub.+2] ...
normalized maximizing
indices
The sums of weighted [S.sub.-1] [S.sub.-2] ...
normalized minimizing
indices
Significance of the [S.sub.-1] [Q.sub.2] ...
real estate
Real estate's [Pr.sub.1] [Pr.sub.2] ...
priorities
Real estate's utility [N.sub.1] [N.sub.2] ...
degree (%)
Criteria Real estate to be valued and
comparable real estates
[a.sub.j] ... [a.sub.n]
[X.sub.1] [d.sub.1j] ... [d.sub.1n]
[X.sub.2] [d.sub.2j] ... [d.sub.2n]
... ... ... ...
[X.sub.i] [d.sub.ij] ... [d.sub.in]
... ... ... ...
[X.sub.t] [d.sub.tj] ... [d.sub.tn]
... ... ... ...
[X.sub.t+1] [d.sub.t+1j] ... [d.sub.t+1n]
[X.sub.t+2] [d.sub.t+2j] ... [d.sub.t+2n]
... ... ... ...
[X.sub.i] [d.sub.ij] ... [d.sub.in]
... ... ... ...
[X.sub.m] [d.sub.mj] ... [d.sub.mn]
The sums of weighted