Fuzzy System Model to Assist with Real Estate Appr

to Assist with Real Estate Appraisals

Dariusz Kr´o l1,Tadeusz Lasota2,Wojciech Nalepa,and Bogdan Trawi´n ski1

1Wroc l aw University of Technology,Institute of Applied Informatics,

Wybrze˙z e S.Wyspia´n skiego27,50-370Wroc l aw,Poland

{dariusz.krol,trawinski}@pwr.wroc.pl

2Agricultural University of Wroc l aw,Faculty of Environmental Engineering and Geodesy,C.K.Norwida25/27,50-375Wroclaw,Poland

tadeusz.lasota@wp.pl

Abstract.Real estate appraisal requires expert knowledge and should

be performed by licensed professionals.Prior to the evaluation the ap-

praiser must conduct a thorough study of the appraised property i.e.a

land parcel and/or a building.Despite the fact that he sometimes uses

the expertise of the surveyor,the builder,the economist or the mortgage

lender,his estimations are usually subjective and are based on his ex-

perience and intuition.The primary goal of the paper is to present the

concept of a fuzzy rule-based system to assist with real estate appraisals.

The input variables of the system comprise seven attributes of a property

and as the output the system proposes the property’s value.For the ap-

praisal area,so called representative property is determined and in fact

the deviations of property attribute values from the representative ones

are the input into the fuzzy system.The proportion of the representative

property price to the value of the property being assessed is produced as

the output of the system.The experts have built the Mamdani model of

the system,however they have not been able to construct the rule base.

Therefore an evolutionary algorithm has been employed to generate the

rule base.The Pittsburgh approach has been applied.The learning pro-

cess has been conducted using training and testing sets prepared on the

basis of150sales transactions from one city.

1Introduction

There are three most common approaches to determining the market value of a property:a cost approach,a sales comparison approach,and an income ap-proach.The appraiser chooses an appropriate approach,methods and techniques taking into account such criteria as the goal of the evaluation,the type of a property,its location,its purpose,transaction prices,etc.The most popular is sales comparison approach.Applying this approach it is necessary to have transaction prices of the properties sold which have attributes similar to the one being appraised.If good comparable transactions are available,then it is possible to obtain reliable estimates.Prior to the evaluation the appraiser must conduct a thorough study of the appraised property using available sources of

H.G.Okuno and M.Ali(Eds.):IEA/AIE2007,LNAI4570,pp.260–269,2007.

c Springer-Verlag Berlin Heidelberg2007Fuzzy System Model to Assist with Real Estate Appraisals261 information such as cadastral systems,transaction registers,market analyses, and on-site inspection.Despite the fact that he sometimes uses the expertise of the surveyor,the builder,the economist or the mortgage lender,his esti-mations are usually subjective and are based on his experience and intuition. Automated valuation models(AVMs)are being more and more accepted.These are based on statistical models such as multiple regression analysis,soft com-puting methods and geographic information systems(GIS)[2].A series of meth-ods based on artificial intelligence have been developed to support appraisers’works.Among them are artificial neural networks[4],[5],[13],data mining[12], neurofuzzy networks[11],case-based reasoning[6],and hybrid soft computing methods[1].

The primary goal of the paper is to present the concept of a fuzzy rule-based system assisting the real estate appraisal.The input variables of the system comprise seven attributes of a property and as the output the system proposes the property’s value.For the appraisal area,so called representative properties are determined and in fact the deviations of property attribute values from the representative ones are the input into the fuzzy system.The proportion of the representative property price to the value of the property being assessed is produced as the output of the system.The experts have built the Mamdani model of the system.However they have not been able to construct the rule base.Therefore an evolutionary algorithm has been employed to generate the rule base.The Pittsburgh approach has been applied[8].The overall structure of the evolutionary algorithm used in the experiments conformed to the structure of a classic genetic algorithm,but a different way of coding chromosomes and a modified crossover and mutation operations were applied.The extensive overview of genetic fuzzy systems can be found in[3],[7].

2Information Systems Aiding Real Estate Appraisal

The fuzzy system assisting real estate appraisal is devoted to an information centres maintaining cadastral systems and property sales transaction registries. Due to the substantial dispersion in Poland,these systems are located in dis-trict local self-governments as well as in the municipalities of bigger towns,and there are above400such centres all over the country.All three systems to-gether could create a complex data source for real estate appraisers accessi-ble through internet(see Fig.1).At present the information centres are the place which appraisers contact when they start evaluating properties.Moreover the appraisers are obliged to deliver the results of their estimates to the gov-ernmental registry of real estate transactions.Therefore the actual values and prices of properties are available in the registry.On the basis of data taken from the registry and the cadastral system the initial parameters of the fuzzy system aiding real estate appraisal can be determined such as the sections of comparable characteristics and the representative properties for each land section.262 D.Kr´o l et al.

Fig.1.Information systems aiding real estate appraisal

3Fuzzy Model for Real Estate Appraisal

The fuzzy system for real estate appraisal has been based on sales comparison method.It has been assumed that whole appraisal area,that means the area of a city or a district,has been divided into sections of comparable property attributes.As the most important attributes location and land use characteristics were regarded.An adequate representative property as well as the parameters of fuzzy sets and rule bases have been determined for each section.

The architecture of the fuzzy system aiding real estate appraisal has been shown in Fig.2.The appraiser accesses the system through internet and chooses an appropriate section and input the values of the attributes of the property being evaluated.

Then the system using the parameters of the representative property for the section indicated,calculates the input values to the fuzzy model.The classic fuzzy inference mechanisms,applying a proper rule base,calculates the output. Then on the basis of the parameters of the representative property thefinal result is determined and as a suggested value of the property is sent to the appraiser.

Fig.2.Architecture of the fuzzy system for real estate appraisalFuzzy System Model to Assist with Real Estate Appraisals263 The Mamdani model for real estate appraisal has been built with the aid of experts.It has comprised7input variables and each of them referred to the difference or proportion of attribute values between a property being appraised and the representative one.The representative properties have been determined for each section,having similar characteristics,by means of calculating average values of attributes of all properties in the training set of data used in the experiment.For each input variablefive triangular and trapezoidal membership functions have been defined and for output-nine(see Fig.3.).Therefore the input of the fuzzy system is defined by the vector of seven following variables:

–Distance-it is the difference in the distance from a local centre expressed in meters.The domain of this variable is the interval form-1000to1000 meters.Negative values denote that the representative property is located closer to the local centre than the appraised one.

–Front-it is the difference in the length of fronts of parcels expressed in meters.The domain of this variable is the interval form-50to50meters.

Positive values mean that the examined parcel has longer front than the representative one what is considered as a better result.

–Area-it is the ratio of the area of the examined parcel to the area of the representative one.The domain of this variable is the interval form0to10.

Values greater than1indicate that the examined property has the bigger area.

–Infrastructure,arrangement neighborhood and communication-values of these four attributes are appraiser’s judgments of what is the difference in

a given attribute between the appraised and the representative parcels.The

values are taken from the range0-200where100means that both parcels are equal in this respect,values greater than100-that the examined parcel is better and the ones lower than100-the opposite.

–Infrastructure-refers to what extent the technical infrastructure of a given property is better than the representative one.

–Arrangement-pertains to the assessment of how better a given property was arranged than the representative one.

–Neighborhood-concerns the difference in the quality of properties’neigh-borhood.

–Communication-deals with the evaluation of the means of public trans-portation available to the residents.

The output of the system is the ratio of the property value being appraised to the value of the representative one.The linguistic values are as follows:very much lower than(VMLT),much lower than(MLT),lower than(LT),slightly lower than(SLT),equal(EQ),slightly greater than(SGT),greater than(GT), much greater than(MGT)and very much greater than(VMGT).

4Learning Fuzzy Rules by an Evolutionary Algorithm Constructing the fuzzy model with7input variables,the experts have not been able to construct the rule base.Therefore the evolutionary algorithm has been2 D.Kr´o l et al.

Fig.3.Membership functions of input and output variables

employed to generate the rule base and the Pittsburgh approach has been ap-plied.The learning process has been carried out employing the MATLAB soft-ware tools.Some preliminary tests revealed that it was very hard to carry out experiments employing a classic genetic algorithm to assure acceptable execu-tion time using available hardware,therefore a modified evolutionary method has been used.The structure of an evolutionary algorithm is the same as the structure of a classic genetic algorithm[11](see Fig.4),but the algorithm applied differs in the way of chromosome coding and crossover and mutation operations.

Training and testing sets.The set of data used in the process of generating rules comprised150sales transactions made in one of Polish cities and located in residential sections what assured comparable attributes of properties.The dataFuzzy System Model to Assist with Real Estate Appraisals265

Fig.4.Structure of the evolutionary algorithm

were taken from the governmental registry of real estate sales transactions.The attributes of the properties embraced by those transactions were determined by an expert,who had visited and studied personally all of them.The set of data was bisected into learning and verifying sets by clustering the property descriptions including their prices using the k-means method and then by splitting randomly each cluster into two parts.Finally the training data set counted77properties and the verifying one73properties.

Fig.5.Coding scheme:a)three rules encoded by natural numbers and b)the fragment of a resulting chromosome

Coding chromosomes.The rule base was coded using the Pittsburgh method, where one chromosome comprised whole rule base.We assumed constant length of the chromosome composed of n rules.Each i-th rule was represented by8 bytes:b1i,b2i,...,b8i,wherefirst seven bytes contained natural numbers from1to 5corresponding to linguistic values of seven input variables(see Fig.5),e.g.MLT (much less than),LT(less than),EQ(equal),GT(greater than),MGT(much greater than)respectively.Zero value on the position of a given input meant that this attribute did not occur in the rule.The8-th byte represented the output and could contain natural number randomly taken out of the range from1to9 referring to linguistic value of the output:VMLT(very much less than),MLT

(much less than),LT(less than),SLT(slightly less than),EQ(equal),SGT (slightly greater than),GT(greater than),MGT(much greater than),VMGT (very much greater than)respectively.

Initialization.At the beginning the space of all possible rules was confined to that comprising only those rules which could be activated by the set of training data.Let us call this set as activated rules.Then each chromosome was composed of rules taken randomly out of the activated rules and so the initial population of randomly generated chromosomes was obtained.

Fitness function was calculated as an average error between values of prop-erties included in the training set and the values of corresponding properties determined by the fuzzy system using a rule base produced by a subsequent generation of the evolutionary algorithm.

Crossover.Uniform crossover operation was employed,where the pattern of the position of rules to be exchanged was determined randomly for each pair of parents separately with the probability of0.5.According to this pattern whole rules were exchanged between the parents of a given pair instead of individual genes.In Fig.6it is shown that i-1-th and i+1-th rules are exchanged between parent chromosomes.

Fig.6.Crossover operation a)parents,b)crossover pattern,c)offspring Mutation.During the experiment we noticed that our algorithm converged faster when operator of mutation was modified.Instead of altering individual alleles in a randomly selected chromosome with the probability of0.07,we removed it entirely from the population and replaced it by a completely new chromosome composed of the rules taken randomly from the set of activated rules. Results.Preliminary experiments were conducted with different number of rules in one chromosome i.e.5,20,50,100and250and different size of population counting100,250and1000chromosomes.In Table1the values of thefitness function for the best combinations of chromosome length and population size, which resulted in the lowest values,are presented.The table header indicates the combination of the number of rules in a chromosome(100or250)and the

Fig.7.Relative error distribution for training and testing sets

size of a population(250or1000).For each combination test run was repeated 3times and stopped after40generations of the evolutionary algorithm.

Table1.Values offitness function for different parameters of an evolutionary algorithm

Test no.100/1000250/250250/1000

125,5930,8731,90

239,7236,7827,52

318,45*17,6815,42

Table2.Mean absolute and relative errors for selected rule base

Set of data Mean absolute

error

Std dev.of

absolute error

Mean relative

error

No.of outliers

training18,4627,718%0 training and testing26,4636,2911%4 testing34,53,4814%4

For the rule base obtained in test number3for100rules in a chromosome and the population of1000(one marked with an asterisk in Table1)the suggested prices for all properties constituting training and testing sets were determined by means of the fuzzy model defined in the MATLAB software tool.Then absolute and relative errors with reference to real prices were calculated for each property. Properties,for which an absolute error was above50%,were regarded as outliers and discarded from further calculations.In Fig.7the distribution of relative errors for training and testing sets is shown.In Table2the resulting mean absolute and relative errors are presented.The results obtained are promisingbecause the mean relative errors were rather low and for the testing set it was equal to14%.Nevertheless further investigations are needed for greater number of generations of an evolutionary algorithm as well as for different parameters of fuzzy model and evolutionary algorithm.

5Conclusions and Future Work

The Mamdani fuzzy model for assisting the property appraisers’work was pro-posed in the paper.The model comprises7input variables referring to the attributes of a property being evaluated.As an output it produces the sug-gested price for a given property.Rule base of the model was generated and optimized using an evolutionary algorithm based on Pittsburgh approach.The results of learning rule base are promising,despite they were achieved for a rel-atively small number of generations performed by an evolutionary algorithm. This encouraged us to plan further investigations with different parameters of fuzzy model and evolutionary algorithm.It will be worth to investigate how sim-plifying the model by means of removing the least important input variables will influence the accuracy of the fuzzy model and what degree of accuracy will be required to be acceptable to users.Training and testing sets could be revised in order to detect and exclude possible outliers.We intend to construct the equiv-alent TSK fuzzy model and carry out experiment to compare the results with those obtained using Mamdani one.It is also planned to implement the model and to deploy it in one information centre.

References

1.Bonissone,P.P.,Chen,Y.-T.,Goebel,K.,Khedkar,P.S.:Hybrid soft computing

systems:industrial and commercial applications.In:Proceedings of the IEEE,vol.

87(9),pp.11–1667(1999)

2.Castle,G.H.:GIS:Meeting the Information Demand.Valuation Insights and Real

Estate Investor42(1),66–71(1998)

3.Cord´o n,O.,Gomide,F.,Herrera,F.,Hoffmann,F.,Magdalena,L.:Ten years of

genetic fuzzy systems:current framework and new trends.Fuzzy Sets and Sys-tems141,5–31(2004)

4.Do,Q.,Grudnitski,G.:A Neural Network Approach to Residential Property Ap-

praisal.Real Estate Appraiser,pp.38–45(December1992)

5.Evans,A.,James,H.,Collins, A.:Artificial Neural Networks:An Application

to Residential Valuation in the UK.Journal of Property Valuation and Invest-ment11(2),195–204(1991)

6.Gonzalez,A.J.:A case-based reasoning approach to real estate property appraisal.

Expert Systems with Applications4(2),229–246(1992)

7.Herrera,F.:Genetic Fuzzy Systems:Status,Critical Considerations and Future

Directions.International Journal of Computational Intelligence Research1(1),59–67(2005)

8.Hoffmann,F.,Pfister,G.:Evolutionary design of a fuzzy knowledge base for a mo-

bile robot.International Journal of Approximate Reasoning17(4),447–469(1997)9.McCluskey,W.J.,Anand,S.:The application of intelligent hybrid techniques for

the mass appraisal of residential properties.Journal of Property Investment and Finance17(3),218–239(1999)

10.Nalepa,W.:Fuzzy Expert System for Real Estate Appraisal.M.Sc.Thesis(in

Polish).Wroc l aw University of Technology(2006)

11.Rutkowski,L.:Methods and techniques of artificial intelligence(in Polish).PWN

Warsaw(2005)

12.Soibelman,L.,Gonz´a lez,M.A.S.:A Knowledge Discovery in Databases Frame-

work for Property Valuation.Journal of Property Tax Assessment and Adminis-tration7(2),77–106(2002)

13.Worzala,E.,Lenk,M.,Silva,A.:An Exploration of Neural Networks and Its Ap-

plication to Real Estate Valuation.The Journal of Real Estate Research10(2), 185–201(1995)