Mass appraisal of real estate and fuzzy numbers in Belarus

Nikolai Siniak

Associate professor of Belarusian State Technological University,

Member of gif German Society of Property Researchers

E-mail:

siniakn@mail.ru

siniakn@tut.by

“Paper presented at the seminar ”Advances in mass appraisal methods”, Delft, The Netherlands, 30-31, October, 2006. 2

Mass appraisal in Belarus used mostly for

taxes

Mass appraisal

Land

(official mass appraisal)

Flats

(scientific work)

Purpose of the research is with a help of existing examples (Belarusian

experience of mass valuation) to find a disadvantages of traditional approaches

in mass appraisal and consider a possibilities to use fuzzy system in mass

appraisal. We come to the conclusion on the existing stage of development

fuzzy system that we should combine traditional statistic approaches (for

example multyregression techniques) with fuzzy logic and neural system. We

can use fuzzy in individual valuation or in mass appraisal if the valuation of

factors is making at time, when their future estimation is labored (has not a

sufficient probabilistic bases). We also should develop fuzzy approaches and

methods and first of all computers fuzzy technologies. It is necessary to

develop big the program "of fuzzy researches directed on achievement by

valuation and real estate economy sphere of a qualitatively new level of

self-consciousness”. These questions can be solved, if it is created and within 2-3

years minimally financed working group of the researchers in area Fuzzy Sets

and Control.

208 cities and

towns

24 000 villages

It was completed cadastral

valuation of the lands of

5 000 garden

companies

4

• The Main methdological principle

of the methods cadastral valuation

of the town lands - an

Briefly technology cadastral

estimations of the lands of the

populated points possible to describe

the following operation (the stage):

• The Stage 1. Shaping the thematic layers to source

information in format ArcView GIS.

• The Stage 2. Merit zoning.

• The Stage 3. The Determination of market value test land

area.

• The Stage 4. The Determination of the base cost of the lands.

• The Stage 5. The Determination cadastr cost of the merit

6

Conclusions of 1

st

part

• Technology of cadastral valuation of

the town lands in Republic Belarus

provides

broad

using

Research purpose of flat mass apprisal

Jointly with Sergio Coppiello (Italy)

8

Analysis model

Mass appraisal

Mass appraisal models

•

The models for mass appraisal are the two following:

•

P =



+



_j

• X

_j

+



[4]

•

P’ =



+



_j

• X

_j

+



[5]

•

where P represent total house prices, P’ house prices per

10

Mass appraisal models

•

In statistical terms [4] and [5] are linear models, which can be

handled with standard regression techniques, namely least

quares estimators and test of significance based on t-statistics.

•

Models are tested both on original variables and on normalized

variables [6], in order to highlight their relative importance:

•

X

_ij

= 2 • (X

_ij

– X’

_j

) / (X

_maxj

– X

_minj

)

[6]

Empirical evidences:

total price model

•

The model results for total price of house are:



P = –13.583 +665 X

+1.056 X

+1.764 X

+31 X

+3.239 X

+



(16,06) (79,87) (13,83) (6,96) (2,89) (11,30)



+2.228 X

–1.272 X

+10.365 X

–983 X

+4.522 X



(4,42) (3,40) (8,12) (3,02) (12,66)

12

Variables of analysis

Variables

P

supply price ($)

P’

supply price ($ per square meter)

X

number of rooms

X

Neighborhood

X

total square meters of flat

X

square meters of the living part

X

square meters of kitchen

X

number of floor of flat

X

number of floors of building

X

flat not at first or last floor

X

age of the building in year

X

prefabricated building

X

brick building

X

cement building

Variables

X

monolith building

X

presence of phone

X

one separate toilet and bathroom

X

one common toilet and bathroom

X

two separate toilet and bathroom

X

two common toilet and bathroom

X

presence of balcony

X

presence of loggia

X

presence of veranda

X

a closed one of X

, X

, X

X

wood as floor surface

• the model can not be ideal, since it is based not

on 100% market information: incorrect deals,

bad database brings about that that in 9 events

model gives close to ideal results, but in tenth -

surge. Particularly this often occurs on unique

object.

14

Reasons of inaccuracy of the valuation

• 1. Analysis market and collection of data is

conducted on the first stage.

• Database is formed on the second stage.

• At this stage, inaccuracy appears at a rate of

formalizations. For example, the factor wall

building is assigned as panel, block, brick,

wood and multifunction wall.

16

• The Third stage - a choice of the type of

• In the step of calibrations appears the last type of

inaccuracy connected with choice of the vector of

initial importances for iterative methods, with number

by cast-off filter data, finally, with number of

iterations.

• In the course of mass valuation of flats it was found

out inaccuracy about 4 %. From the words of mass

valuation specialists inaccuracy is available up 5-10

%.

18

Cadastral value can be defined:

normative method

expert method

• VL = PV + (I - E) : R (*),

CALCULATION of the CAPITALIZED VALUE

Ретроспектива по годам

Parameters of calculation per year

5 year

4 year

3 year

2 year

1 year

rate of the discounts-Kd

17,0%

Real rate of growth of the income on years- G

39,7%

16,6%

10,1%

7,1%

Difference between rate of the discounts and

rate of growth on year

20

On the graph you can see that change the rate of the

discounts or rate of growth on 1% changes importance of the

cost of the valued object on 8-20%. Thereby, mistake in value

of the rate of the discounts in amount more than two percents

brings about appearance of the mistake in the price of the

estimation in 16-40%.

Dependency net capitalized income (Ck) from rate of incom growth on

years (G) and discounting rates (Kd)

230,9 184,7 153,9 131,9 115,4 102,6 92,4 84,0 77,0 71,0 131,9 115,4 102,6 92,4 84,0 77,0 71,0 66,0 61,6 57,7 0,0 50,0 100,0 150,0 200,0 250,0 | 1% | | 2% | | 3% | | 4% | | 5% | | 6% | | 7% | | 8% | | 9% | | 10% |

Rate of ne t income growth on ye ars (G)

Not good statistical explanation

Average price of 1 sq.м. dweling of Мinsk ($)

y = -0,0113x

+ 0,5029x

- 8,5284x

+ 70,938x

-

314,44x

+ 749,15x - 401,32

R

= 0,9923

200

400

600

800

1000

1200

Real estate prices

22

Tendency of growth

0

200

400

600

800

1000

1200

19

92

19

94

19

96

19

98

20

00

20

02

20

04

U

SD

p

e

r

s

q

u

a

re

m

e

te

rs

1000

2000

3000

4000

5000

6000

7000

8000

9000

Eu

ro

p

e

r

s

q

u

a

re

m

e

te

rs

24

Literature research. What kind of fuzzy

is available?

• From "Fuzzy Sets" in 1965 to Perception-Based Theory... "

(Zadeh, 2000).

• "Linear Systems Theory-The State Space Approach"(1963)

"Frequency Analysis"(1950), "Wiener's theory of

prediction"(1950), "Sample-Data Systems"(1952), "Probability

Measures of Fuzzy Events" (1968), "Outline of a new

Approach to the Analysis of Complex Systems and Decision

Processes"(1973), "Fuzzy Sets as a Basis for a Theory of

Possibility"(1978), "A Theory of Approximate

Reasoning"(1979), "The Role of Fuzzy Logic in the

Management of Uncertainty in Expert Systems" (1983),

"Fuzzy sets" (1985) etc. (Zadeh)

• Fuzzy mathematics, cognitive and decision process

were being to be developed by Kaufmann(1975),

Zadeh, Fu, Tanaka, Shimura(1975), Neogita and

Ralescu, (1975).

• D.Dubois and H.Prade, 1980

26

Very simple to use

valuation cost =

(9,2,10,11)/(0,14;0,15;0,16).

D=[9,2+0,8a,11-1a]/[0,14+0,01a,0,16-0,01a]=

=[(9,2+0,8a)/(0,16-0,01a),(11-1a)/(0,14+0,01a)].

It is evident that the property cost is not lower $ 57500 and not above $ 78571.

With 100% certainty, we can state that the cost of the estimated property is $66 666.

28

Disadvantages of fuzzy system:

• 1. Absence of understanding in mass appraisal

specialists.

• 2. Absence of special computer programs

available like Excel. The best way out is to

integrate fuzzy system in Microsoft Office and

Excel.

For mass appraisal

• On the existing stage of development fuzzy system that we

should combine traditional statistic approaches (for

example multyregression techniques) with fuzzy logic and

neural system.

30

Expert’s opinions

Experts

Income (V)

Costs (C)

Net income (I)

We a help of average fuzzy numbers

• Valuation of I expert

• With a help of



-cuts

32

)

636

,

619

,

596

(

)

6360

,

6190

,

5960

(

10

1

1









n

_

i

C

)

96

,

40

,

5

(

)

960

,

400

,

50

(

10

1

1













n

_

i

I

The most probable income is 40. Than we put the figure in formula

* and get exact result. Than we use traditional approaches.

Conclusions

Professor Zadeh

In humanistic systems, human reasoning and decision making is not just

"measurement" based, as we are taught through out our academic education,

rather "perception" based. "Fuzzy Sets" in 1965 and came to surface toward the

beginning of this Millennium in "Toward a Perception-Based Theory... " (Zadeh,

2000).

Conclusion: from the above analysis we can state that the

application of fuzzy numbers in the process of property evaluation

enables to determine property value with much higher probability

(100%) in comparison with the traditional approaches of evaluation

34

We need to work on further developments of fuzzy theory in

particular on fuzzy knowledge representation and reasoning

in real estate field. This is more acutely needed in the

development of humanistic decision making domains which

Professor Zadeh have been urging us to direct our attention

over the last thirty five years or so.

We need to create of an fuzzy economy, valuation and management of real estate

organization. It is aimed to establish an institute, which accepts fuzzy valuation

and economy as a profession, to control and manage the applications in respect

of education, rules and standards. It is also aimed to standardize fuzzy

valuation, approaches, rules and factors which must be taken care during the

fuzzy valuation and management. We also need to provide by methodology and

standards valuers and mass appraisal issues and define the role fuzzy valuation

in investment decision-making process.

36

Welcome to Belarus

You will have a chance to see some from Belarusian

architecture and hospitality of Belarusian people.

Conferences:

1. International real estate conference

15-17 November 2006, Minsk

For more detail: www.expozona.lt

2. The 2-d International Conference

ECONOMY, VALUATION AND MANAGEMENT OF THE REAL ESTATE AND

NATURAL RESOURCES

Minsk, May, 3-5, 2007.

38

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Environment”, Management Science (17), pp. 141- 164,

(1970)

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338-353, (1965)

• 3. Zadeh L.A., The concept of a linguistic variable and

its application to approximate reasoning I, II, III, Inf.

Sci., 8(1975),199-257, 301-357; 9(1975), 43-80.

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I.BURHAN TÜRKŞEN. Operations Research and

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University of Toronto, 2000.

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Theory of Probabilistic Reasoning", Key note

address; Fourth International Conference on

Applications of Fuzzy Systems and Soft

Computing, June 27-29, Siegen, Germany,

40

• 8. Nikolai Siniak. FUZZY NUMBERS FOR THE ASSESSMENT OF

REAL ESTATE MARKET AND PROPERTY VALUATION. Paper at the

8th ERES Conference Alicante, 2001

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European Real Estate Society Conference (ERES 2002), June, 2002,

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