OPTIMAL SPATIAL DECISION MAKING USING GIS: A ... - CiteSeerX

- 428 -

OPTIMAL SPATIAL DECISION MAKING USING GIS: A PROTOTYPE OF A REAL ESTATE GEOGRAPHICAL INFORMATION SYSTEM Thomas Q. Zeng PhD Student, Department of Geography, University of Sydney Building HO3, City Road, Sydney 2006, Australia Phone: (612) 935517668; Fax: (612) 93513644; E-mail: [email protected] Qiming Zhou Associate Professor, Department of Geography, Hong Kong Baptist University Kowloon Tong Kowloon, Hong Kong Phone: (852) 23395048; Fax: (852) 23395990; E-mail: [email protected] Abstract: In the real estate business, it is a common understanding that the value and the potential value of a property are fundamentally determined by its location. This emphasises the importance of spatial factor in decision making in real estate. A geographical information system (GIS) is undoubtedly useful in this aspect. This paper reports the development of a prototype real estate GIS (REGIS) by integrating a rule-based system (RBS), fuzzy set (FZ) theory and GIS. The role of this system in the real estate business is to assist decision making for sellers and buyers, as well as the property management. For the real estate agencies, the system can be used as an assistant in selling and managing properties. For the buyers, the REGIS can function as a consultant in their decision making in purchasing properties. Methodologies are demonstrated with a case study. Developed as generic tool with capabilities to deal with uncertainties, this prototype can be applied to other fields, which involves optimal spatial decision-making. Keywords: real estate, rule-based system, fuzzy set theory, GIS INTRODUCTION Optimal spatial decision-making (OSDM) is a branch of decision-making (DM) science. In general, OSDM involved analysis of factors and constrains that affects the decision-making. It requires handling a substantial amount of data and utilising expert knowledge. Geographical information system (GIS), specially designed for handling spatial data, is certainly capable of performing the tasks. However, despite long history of DM theories and applications, (e.g. Lowry, 1964; Gaile and Wilmott, 1984; Parker and Rardin, 1988; Maier, 1993; and Daskin, 1995), OSDM using GIS only emerged recently. Studies were reported, for example, in waste site selection (Zhou and Charnpratheep, 1996; and Charnppratheep, et al., 1997), urban studies (Carver 1991; and Reitsma, 1990), locating public facilities (Fortney, 1996) and real estate (Wyatt, 1997). In general, there are two main streams in OSDM. One is aimed to find out optimum locations for activities over a network (e.g. the network-based location-allocation analysis). The other is for the best locations by evaluating specified criteria (site-selection). This paper focuses on the latter with particular interest in the real estate.

Zhou, Q., Li, Z., Lin, H. and Shi, W. (eds.) Spatial Information Technology Towards 2000 and Beyond The Proceedings of Geoinformatics'98 Conference Beijing, 17-19 June, 1998, pp. 428-438

Copyright  1998 The Association of Chinese Professionals in GIS - Abroad 151 Hilgard Hall, University of California, Berkeley, CA 94720-3110, USA All rights reserved. ISBN 0-9651441-5-1 Printed in Beijing, P. R. CHINA

OPTIMAL SPATIAL DECISION MAKING USING GIS

429

The objective of this study is to develop a methodology and prototype real estate GIS (REGIS) for OSDM in the real estate industry. This is done by incorporating the existing DM theories, fuzzy set (FZ) theory and rule based system (RBS) into a GIS operating environment. The REGIS is to serve two applications: 1) For real estate agents, it is used as a tool for assisting property selling and management. 2) For purchasers, it serves as a consultant that locates initial potential area, and evaluates available choices by weighting functions according to the customer's preferences. FRAMING THE PROBLEMS A property can be referred to as an unmoveable (mostly, if not all) commodity that exists in physical and social space. Its location, as well as price, is premier factor that affects decision making in property selection. In real estate, questions are often asked, for example, “Where to find the house I like?” – a question related to physical and social environment. “Which is the best property to buy?” – a question referred to individual preferences. In the first question, “where” refers to “location” that implicates the property environment in physical and social spaces. In the second question, “the best”, referring to “the most suitable” or “the optimum”, is subject to purchaser’s preference. The answer to this question depends upon the purchaser’s choice of workplace, personal income, and house tenure within metropolitan area (Simpson, 1987; Waddell, 1993). Furthermore, it also depends upon the purpose of purchases, e.g. livein, sole investment, or both. Therefore, in order to answer the questions, the REGIS should provide two main functions, namely, systematic analysis of physical and social environment and mapping the potential area, and financial assessment of the target properties of the purchaser’s choices. DATA AND METHODOLOGY Data Data used for OSDM should be representative of physical and social environment, and easy to obtain. Ideally, the basic factors that cover most of essential aspects in finding an optimal site include: Physical factors: slope and aspect, vegetation density, parks and natural reserves, rivers and beaches. Social factors: shops and shopping centres, railway stations, schools, hospital, theatres roads, bus stops, railway, power-lines, aeroplane noise, house price and other population data surveyed by census. Personal factors: income, place of work, location of relatives’ residence, number of heads in a household, and the amount of housing loan. Considering the nature of the application and data availability in this study, a simplified version of these factors was used as the main selection criteria: • Physical environment (slope and aspect, parks and natural reserves, rivers and beaches) • Amenity and transport (shops and shopping centres, schools and railway stations) • Pollution and noise (main road pollution and noise, railway noise, aeroplane noise) • Repayment time (loan, income and transport cost) • Potential value increase (price trend)

PROCEEDINGS OF GEOINFORMATICS’98 CONFERENCE, BEIJING, 17-19 JUNE 1998

430

ZENG, T.Q. AND ZHOU, Q.

Methodology System configuration The integration of FZ and RBS with GIS offers a great potential for enhancing our ability in OSDM (Sui, 1994). A multiple-component model was developed by incorporating several methods and techniques as described in Burrough, et al., (1992); Wang et al., (1990), Zhou and Charnpratheep, (1996), and Charnpratheep, et al., (1997). The system has four components, namely, grid modelling, network analysis, information manipulation and random simulation (Figure 1).

Figure 1. System structure of Real Estate GIS

The grid modelling functions are tools for analysing physical and social factors to produce potential area map. The network analysis aims to measure the distance between residence and work, shops, school and public transport. The information manipulation is to calculate repayment and compare different alternatives financially. The random simulation is used to estimate the future trend in house price. GIS functions supported by ARC/INFO GIS software were incorporated with fuzzy calculations that were implemented using ARC/INFO's Arc Macro Language (AML). Other relevant information, such as house price, house loan, calculation of repayment time, was handled by INFO Data Base Management System (DBMS). Selection Procedures Optimal site selection, as described in DM theories, usually involves two stages: in preliminary stages, candidate sites are selected using the FZ screening process. At the second

SPATIAL INFORMATION TECHNOLOGY TOWARDS 2000 AND BEYOND

OPTIMAL SPATIAL DECISION MAKING USING GIS

431

stage, the selected sites are compared with each other and ranked according to their attractiveness. Through the screening process, the potential areas are mapped to identify target sites. In this stage, grid modelling is used with FZ analysis using an approach demonstrated by Charnpratheep, et al. (1997). Once the candidate sites is selected, the attributes for each site are assessed using the RBS for network analysis, information manipulation, and random simulation. The attribute values, expressed in FZ, are summarised in a table with commendation by the RBS. FUZZY SET AND FUZZY RULE BASED SYSTEM Fuzzy Set The term of fuzzy set is coined by Zadeh (1965), as a generalised form of set theory. Unlike the traditional Boolean logic which defines either or not an element belongs to a crisp set (1 or 0), fuzzy set defines it into a degree of belonging through a membership function. Let X be a universe of discourse having its generic elements x, or X = {x}. A fuzzy set F in X is characterised by a membership function, µF(x), that maps X to the membership space [0, 1]. µF(x) represents the grade of membership of x in F. For continuum and discontinuum X ={x}, the fuzzy set can be expressed as Equation 1 and Equation 2, respectively. F = ∫ µ F ( xi ) / xi

(1)

X

F = {µ F ( xi ) / xi } (2) In essence, fuzzy set theory is aimed at dealing with sources of uncertainty or imprecision that are indecently vague and non-statistical in nature. Its main aim is to develop a methodology for the formulation and solution of problems that are too complex or ill defined to be susceptible to analysis by conventional techniques. Details about fuzzy set, fuzzy algorithms and its applications can be found in Kaufmann and Zadeh, 1975; Zimmermann 1991; Terano et al. 1992; Bezdek 1992, and Kasabov, 1996). The FZ approach for site selection in real estate has two aspects. One is to handle the fuzziness in spatial distribution of a physical or social factor (fuzzy boundary) and the other is to handle fuzziness in query with a RBS (fuzzy inference). In this study, the selection criteria that were expressed in ambiguous terminology are codified with FZ, of which membership functions are based on the ‘common sense’ as well as expert knowledge. The general fuzzy membership function (Equation 1 and 2) can be implemented into three types: the linear, “S” and logarithm functions (Kaufmann and Gupta, 1988). While user’s specifications are allowed, the default fuzzy membership functions for each factor and sub-factors in terms of ‘good location’ are defined as follows. The linear function:  1   b − x µ F (x ) =  b − a   0

0≤ x≤a a< x≤b b< x

PROCEEDINGS OF GEOINFORMATICS’98 CONFERENCE, BEIJING, 17-19 JUNE 1998

(3)

432

ZENG, T.Q. AND ZHOU, Q.

• • • • •

Close to beach (a = 100 m, b = 1500 m) Close to parks and reserves (a = 60 m, b = 700 m) Close to schools (a = 500 m, b = 1500 m) No railway noise (a = 30 m, b = 200 m; and using F’ (X) = 1 - F (X)) Good aspect: The value of aspect ranges from 0° – 360°. Based on the geographical location of the study area, they are subdivided three intervals with different linear equation:

 x  450 + 0.8   x     µ F ( x ) = 1.251 − 225        x  1.5 225 − 1 

0° ≤ x ≤ 45° 45° < x ≤ 225°

(4)

225° < x ≤ 360°

The “S” function: 1    a +b  1 1  π  µ F ( x ) =  − sin   x − 2   2 2  b − a    0 

0≤ x≤a a 200m.

SPATIAL INFORMATION TECHNOLOGY TOWARDS 2000 AND BEYOND

OPTIMAL SPATIAL DECISION MAKING USING GIS

433

Some other factors also affect the house price (e.g. the nature of the society). However, this aspect is beyond the scope of this paper thus will not be discussed here.

Fuzzy Rule Based System A fuzzy rule-based system (FRBS) is a RBS with a collection of fuzzy membership functions and rules that are used to reason about data. In contrast to a conventional RBS, which uses Boolean logic and mainly adopts symbolic reasoning, the FRBS uses fuzzy arguments and numerical inference processing. The FRBS for real estate is established in four main steps: a) Defining a rule system and its properties. The rule system R is the set of rules. R ⊇ Bi ,k = (I Ai ,k )

If Ai ,1 I Ai , 2 , L , I Ai ,k = Bi ,k

for i = 1, ..., n

where Ai,k is Rule i, k is factor k, and 'I' means 'AND'. b) Stating the necessary and sufficient conditions for a set of rules to encompass all possible “if ...then...” statement and put into a fuzzy relation matrix. c) Selection of a resulting membership function. d) Defuzzification (optional).

Site Assessment Site Assessment is to evaluate all aspects of each target selected from the screening process. To evaluate the suitability, it can be done in two ways. One is directly to compare the fuzzy membership value for each property from the target map. Another is to use FRBS that analyses all the data layers and to provide a recommendation. Network analysis is used to find out the distances between the target properties and work, school and shopping centre. Frequency of travelling is also considered in calculation of travelling expenses, which is therefore computed as: N

E = k ∑ d i fi

(7)

i =1

where E is the expense for transportation, di is the distance of travelling, fi is the frequency of travelling (times/week) and k is the rate of cost per kilometre. Difference in travel expense for each target property is calculated and put into principal repayment for the loan to calculate repayment time. Random simulation is conducted with parameters based on empirical analysis. This function is optional because of too many uncertainties in the future economics. Sensitivity analysis is regarded as the study of the correlation and calibration between the input parameters, configuration of components, and the expected outcome of the system. Many methods are developed, such as Maximum likelihood, Chi-Square Test, KolmogrovSmirnov Test, and Weighting. Weighting is one of the most commonly used, which assigns different weights (or scale factor) to input parameters in order to test the sensitivity (respond) of the output. In this study, The weighting method was used to produce different scenarios according to the user’s preference. As purchasers are at different stage in their live cycle, they have different priorities in selecting properties. Some may prefer good physical environment, and

PROCEEDINGS OF GEOINFORMATICS’98 CONFERENCE, BEIJING, 17-19 JUNE 1998

434

ZENG, T.Q. AND ZHOU, Q.

“closer to parks and natural reserves”, while others may prefer a handy location that is “close to school”. The weighting function is defined as: n

W = ∑ wi k i

(i = 1, 2, 3, ... , n ;

i =1

∑w

i

= 1)

(8)

where k is a factor, w is the weight, and i denotes the factor number.

THE CASE STUDY The Study Area The study area locates at St George District, southern Sydney, Australia. It covers an area of 21.5 × 16 km with a diversity of environment, resident density and constant growing property market.

Target Area Map The procedure of producing the target area map is as follows: a) Buffering each theme to obtain the proximity in distance. b) Assigning a fuzzy set membership to each pixel using algorithms described above. c) Conducting fuzzy operation for some sub-factors. For example, the aeroplane noise is the combination of noise distribution around the airport and along the fly-path, with the MAX operator. d) Assigning weights for each factor and its sub-factors using a clustered hierarchy structure: 3  n  R = ∑  wi ∑ wi , j µ F ( x )i , j  (9) i =1  j =1  Where R is the resultant fuzzy membership, µF(x)i,j is fuzzy membership function for subfactors j of factor i; wi,j is the weighting function of sub-factor j of factor i; and wi is the weighting function of factor i. In this study, equal weights (wi,j) are assigned for each sub-factor, while weights (wi) for the factors are based on the user’s preference. Since the purchaser’s priorities vary from one to another, the target maps are “customermade” based on each set of preferences. Figure 2 shows the scenarios of potential area according to user’s preferences. In this study, four scenarios were produced by four different trails. a) “No Noise and pollution” is a little more important than physical environment and amenity. b) “Amenity” is most important. c) “Good physical environment” and “no noise and pollution” are preferred. d) “Good physical environment” has a high priority with less concern about “noise and pollution”.

SPATIAL INFORMATION TECHNOLOGY TOWARDS 2000 AND BEYOND

OPTIMAL SPATIAL DECISION MAKING USING GIS

Figure 2. Scenarios of potential memberships.

PROCEEDINGS OF GEOINFORMATICS’98 CONFERENCE, BEIJING, 17-19 JUNE 1998

435

436

ZENG, T.Q. AND ZHOU, Q.

Optimal Site Selection Three target sites were selected and their evaluation is shown in Table 1. The transportation cost is calculated based on the assumption that the purchaser drives a car with a 2.2-liter capacity to work. The fuel price is A$0.70 per liter. In this example, the house loans for option 1, 2 and 3 are A$180,000, A$200,000 and A$190,000, respectively. At the current interest rate of 6.49% pa, the monthly repayments are A$1,214, A$1,349 and A$1,281, respectively, based on a 25-year repayment plan. The differences in travel costs are added on the repayments to give the estimated pay-off time. Table 1. Assessment on the selected target sites.

Option 1 2 3

Physical Environment 0.394 0.311 0.708

Amenity 0.677 0.662 0.48

No noise and Pollution 0.333 0.619 0.333

Total score 1.394 1.592 1.521

Distance to work (km) 29.94 31.02 37.88

Pay-off time (year) 20 25 22

DISCUSION AND CONCLUSIONS Location is a critical factor that affects real estate value. This system provides assessment of location in a broad scale thus improving the real estate agent's awareness of local physical environment that may influence the property value. Different scenarios can be presented and evaluated in terms of resultant daily expenses and repayment term. These will undoubtedly be of great help in assisting real estate business, not only for the selling, but also for the optimum purchasing decision-making. Since different buyers would have different preference, this system can reason out different optimal solutions for different buyers. Searching a property to purchase can be a very stressful process. From buyers’ point of view, in the seeking stage, this system allows buyers’ preference to be considered in selection and can provide them a map of potential areas that meet their requirements. This will significantly save time and travelling, reducing their stress. Secondly, most of the buyers do not have much knowledge about locational influence on property value and physical environment, which could be a hidden pitfall in the selection. This system, by using expert knowledge, can help them to avoid the potential pitfall and provides a more objective opinion in their purchase. Further research can be focused on two aspects: i) to consider multi-householders with respects to the network analysis, route could also considered number of travel fractions (the satellite lights) and can adopted the route planning model proposed by McCalla, et al., (1982), in which routes are conceived as sequence of instructions for how to travel; ii) to incorporate with the Huff’s model (Huff, 1962) to assess the amenities of particular location of residence. The Huff’s model is a probabilistic retail gravity model describing the process by which potential customers choose from among acceptable alternative retail centres to obtain specific goods and services. It suggest that areas of competition between shopping centres overlap, thus shopping trips must be apportioned among competing accessing centres in a probabilistic manner. In selecting property, the inverse result of the Huff model can be used to assess the amenity factors for specified location. In an broad sense, through integrating with other available data (e.g. census data) and other spatial modelling techniques developed over the last twenty years, e.g. Gordon and Vickerman (1982), Huff (1984), Densham and Rshon (1988), Axhausen and Gälling (1992),

SPATIAL INFORMATION TECHNOLOGY TOWARDS 2000 AND BEYOND

OPTIMAL SPATIAL DECISION MAKING USING GIS

437

Clark (1993), Zhou and Civco (1996) and Turton et al. (1997), this prototype potentially offers far greater analytical power to answer questions concerning spatial decision making or police changes, particularly in a “what-if” framework, and can be applied to wide range of disciplines, such as locating infrastructure, land valuation, town-planning, transportation, strategies assessment, as well as marketing involving site selection.

REFERENCES Axhausen, K.W. and Gälling, T. (1992): Activity-based approaches to travel analysis: Conceptual frameworks, models, and research problems. Transport Review, 12(4), 323341. Carver, S.J. 1991, Integrating multicriteria evaluation with geographical information systems. International Journal of GIS, 5, 321-39. Charnpratheep, K., Zhou, Q. and Garner, B.J. 1997, Preliminary landfill site screening using fuzzy geographical information systems, Waste Management and Research, 15(2), 197215. Clark, W.A.V.(1993): Search and choice in urban housing markets. In T. Garling and R.G. Golledge (eds) Behavior and Environment: Psychological and Geographical Approaches, Ansterdam: Elsevier/North Holland, 298-316. Densham, P. and Rshon, G. (1988): Decision support systems for locational planning. In R.G. Golledge and H. Timmermans (eds), Behavioural Modelling in Geography and Planning. London: Croom Helm, 56-90 Daskin, M.S. 1995, Network and Discrete Location: Models, Algorithms, and Applications, Wiley-Interscience. Gaile, C. and Wilmott, C.J. (ed.), 1984, Spatial Statistics and Models. Dordrecht: Reidel. Gordon, I.R. and Vickerman, R. (1982) Opportunity, preference and constraint: an Approach to the analysis of metropolitan migration. Urban Studies, 19, 247-261. Huff, D.L. 1962. Determination of intra-urban retail trade areas. Real Estate Research Program, University of California, Los Angeles. Huff, J.O. 1984. Distance decay models of residential search. In G. Gaile & C. Wilmoot (eds), Spatial Statistics and Models, New York: Reidel, 345-366. Kasabov, N.K. 1996, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering, Cambridge, Massachusetts: MIT Press. Lowry, I. 1964, A Model of Metropolis. Research memorandum No.4035. Santa Monica, CA: Rand Corporation. Maier, G. 1993, The spatial search problem: structure and complexity, Geographical Analysis 25(3): 242-51. McCalla, G.I., Reid, L. & Schneider, P.K. (1962): Plan creation, plan execution and knowledge execution in a dynamic micro-world. International Journal of Man-Machine Studies, 16, 89-112, Parker, R.G. and Rardin, R.L. 1988, Discrete Optimization, Boston: Academic Press. Reitsma, R.F. 1990, Functional Classification of Space: Aspects of Site Suitability Assessment in a Decision Support Environment, Dissertation, Laxenburg, Austria: International Institute for Applied Systems Analysis. Sui, D. 1992, A fuzzy GIS modeling approach for urban land evaluation, Computers, Environment and Urban Systems, 16: 101-115. Turton, I., Openshaw, S and Diplock, G. (1997): A genetic programming approach to building new spatial models relevant to GIS. In Kemp, Z., (ed), Innovations in GIS 4, London: Taylor & Francis, 89-102.

PROCEEDINGS OF GEOINFORMATICS’98 CONFERENCE, BEIJING, 17-19 JUNE 1998

438

ZENG, T.Q. AND ZHOU, Q.

Zadeh, L.A. 1965, Fuzzy sets, Information and Control, 8: 338-353. Zhou, J. and Civco, D.L (1996): Using genetic learning neural networks for spatial decision making in GIS. Photogrammatic Engineering and Remote Sensing, 62, 1287-1295. Zhou, Q. and Charnpratheep, K. 1996, Fuzzy expert system and GIS for solid waste disposal siting in regional planning, Geographical Information Sciences, 2(1-2), 37-50. Zimmermann, H.J. 1991, Fuzzy Set Theory-and Its Applications (2nd Edition), Massachusetts: Kluwer Academic Publishers.

SPATIAL INFORMATION TECHNOLOGY TOWARDS 2000 AND BEYOND