Rough set theory, value tolerance relation and mass appraisal: The day after

Presentation of the book Kauko T. d’Amato M. (2008) (edited by) Advances in Mass Appraisal Methodology.An International Perspective, RICS Real Estate Series, Blackwell Publisher

Rough Set Theory, Value

Tolerance Relation and Mass

Appraisal: The Day After

Maurizio d’Amato Associate Professor -Property Valuation and Investment 1° Faculty of Engineering - Technical University Politecnico di Bari

scientific website: www.noaves.com

The first meeting gave us the opportunity to compare several different methodologies in mass appraisal. We lived a unique experience in the scientific debate, freely comparing mass appraisal methodologies. Some of them were new, others can be defined traditional approaches.

The added value of our experience is not in the quantitative indicators we compared, but in the willingness to discuss about concept, methodologies and problem of mass appraising.

The comparison as we will read on the book it has been done without any prejudice. I proposed a methodology of mass appraisal/property valuation that may be suitable for property market context without a diffused observations.

A promising field of research may become the relation between mass appraisal methodologies and institutional context. The quality and the process of selection of mass appraisal methodology may be improved by an institutional analysis of market context.

A definition of “efficiency” which drive us out the “quantitative indicators” of Fama may help us to define better differencies in real estate markets. At the moment real estate markets according to Fama’s classification are generally defined as imperfect and we can not appreciate and observe the difference between two different imperfect markets.

Real Estate Researcher are the “imperfect researcher working in an imperfect world” according to the financial world (Galileo fight against Aristotelian – ipse dixit- point of view predominant in the middle age italian universities). We hope to become an indipendent field of research without renting

methodology and theory by other scientific fields

This is a call to robust and free scientists. Be proud to be real estate researcher and find material an methods suitable for our problems, wihtout prejudice.

Something more on Catawba County Data

It must be stressed how RST integrated with the functional extension called Value Tolerance Relation can not be see as a direct competitor of MRA. It can be seen as an alternative tools especially for those

contexts were relationship between price and characteristics even if causal can not be modelled with traditional approaches.

Since the first work on RST was clarified that this method do not give any quantitative information about marginal/hedonic prices

The results of RST and VTR in Catawba County case were unsatisfing but the application of the method was not complete. As one can read in the book the research on RST involved a research line of mine started 6 years ago. In this 6 years I started with the so called “traditional version”.

In the “traditional version” the classes of prices are crisp therefore the rule matched the classes of prices with a two value membership function.

In order to test the standard deviation as a measure of k I developed a simplified version. In this case the I used ROSETTA to catch the rule and Value Tolerance Relation to define the rule suitable for the object. After the results obtained in Bari, Helsinki and in another Dutch country. I tried the application of

INFORMATIVE TABLE

k-threshold determination

Comparison Table. comparing each object with the other in reation to each attribute

Membership table. Each object is related to its class of price (do not fear with so much class of prices)

Lower Approximability calculation

( )

(

( )

)

B

F x F B F z

If z ∈ F ⇒ _µ z = _∈ −R z x ≤ _µ =

Selection

The rule with a lower

approximability superior to lamda may be considered

Object Supporting Rule

Calculation.

Credibility Degree of Rule Calculation.

( )1 minx S( )ρ1

(

(

(

)

)

)

µ ρ = _∈ − ρ µ

REDUCTS

DETERMINATION! QUALITY INDEX?

GENERATING

RULES

Something more on Catawba County Data

V Tolerance Table is the minimum of each comparison

Something more on Catawba County Data

SQM BAL PARK PRICE

1 115 2 1 118.000 2 121 4 0 118.000 3 106 3 0 107.000 4 118 2 1 104.000 Sqm Bal Park 6,480740698 0,9574271 0,5773503 k 6,5 1 0,6 sqm 1 2 3 4 park 1 2 3 4 1 1.0000 0.0769 0.0000 0.5385 1 1.0000 0.0000 0.0000 1.0000 2 0.0769 1.0000 0.0000 0.5385 2 0.0000 1.0000 0.0000 0.0000 3 0.0000 0.0000 1.0000 0.0000 3 0.0000 1.0000 1.0000 0.0000 4 0.5385 0.5385 0.0000 1.0000 4 1.0000 0.0000 0.0000 1.0000 bal 1 2 3 4 1 1.0000 0.0000 0.0000 1.0000 2 0.0000 1.0000 0.0000 0.0000 3 0.0000 0.0000 1.0000 0.0000 4 1.0000 0.0000 0.0000 1.0000 Rj 1 2 3 4 1 1.0000 0.0000 0.0000 0.5385 2 0.0000 1.0000 0.0000 0.0000 3 0.0000 0.0000 1.0000 0.0000 4 0.5385 0.0000 0.0000 1.0000

Decisional Class Attribute Classes of Price Objects 118.000 107.000 104.000 1 1 0 0 2 1 0 0 3 0 1 0 4 0 0 1 118000 107000 104000 M118000 m118000 m107000 m107000 M104000 m104000 1 0.46154 0.00000 0.00000 2 1.00000 0.00000 0.00000 3 0.00000 1.00000 0.00000 4 0.00000 0.00000 0.46154 λ 0.6 121 4 0 118.000 If sqm= ∧bal= ∧ park= ⇒ (11.44) The second is 106 3 0 107.000 If sqm= ∧bal= ∧ park= ⇒ (11.45) Sqm balcony Park Property z to appraise 105 3 0 min( ( ; ))R z ρ Rule n.2 – Object n.4 _{106 3 0} Rj 0.8462 1.0000 1.0000 0.8462

Something more on Catawba County

There are several possible considerations…

We have a little variety of application of RST to mass appraisal.Surely, more than

in the past.

After several applications probably assuming

k as the standard deviation of the

attribute anlaysed may be defined an “interesting” option

.

But we can explore

alternative measures of variability as a measure of k.

The inference of lamda on the final value is still unknown. How it affect automatic

valuation modelling?

Missing Data

It is possible to calculate also rules for real estate samples with missing data. This will be the object of my

next article that will be submitted to a journal interested in a sequel of the chapter of the book.

Until we do not have an informatic tool will be difficult to say a final word on this method. At the moment we can consider the property valuation methodology that need more applicative expereince. It was

surprising to observe how giving a sample without any problem the valuation was carried out and no formal models were required.

Conclusion

We discovered a real estate market depending on institutional context.

Hernando De Soto showed in the last decade the important role of informal economy and how informal economic systems live in the most part of the world. In this context economic decision are made on few information.

We can “wait for a tomorrow” describing the beauty of Mass Appraisal methods they will apply when they become “an efficient market” to the systems having informal economy

We can also solve the problem of everyday world giving relevance to “informal method” in mass appraising for “informal system”. I dream that in the future we see RST as another alternative method together with AHP of Tom of Genetic Fuzzy Rule of Marco Aurelio.