Innovative Applications of O.R.
House selection via the internet by considering homebuyers’ risk
attitudes with S-shaped utility functions
Hui-Ping Ho
a, Ching-Ter Chang
b,⇑, Cheng-Yuan Ku
caDepartment of International Business Administration, Chienkuo Technology University, Changhua, Taiwan, ROC b
Department of Information Management, Chang Gung University, Tao-Yuan, Taiwan, ROC c
Department of Information Management and Finance, National Chiao Tung University, Hsin-Chu, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 18 July 2013 Accepted 4 August 2014 Available online 30 August 2014 Keywords:
Decision support systems Multiple objective programming Fuzzy goal programming Utility functions Risk attitude
a b s t r a c t
The widespread use of the Internet has significantly changed the behavior of homebuyers. Using online real estate agents, homebuyers can rapidly find some modern houses that meet their needs; however, most current online housing systems provide limit features. In particular, existing systems fail to consider homebuyers’ housing goals and risk attitudes. To increase effectiveness, online real estate agents should provide an efficient matching mechanism, personalized service and house ranking with the aim of increasing both buyers’ satisfaction and deal rate. An efficient online real estate agent should provide an easy way for homebuyers to find (rank) a suitable house (alternatives) with consideration of their different housing philosophies and risk attitudes. In order to comprehend these ambiguous housing goals and risk attitudes, it is also indispensable to determine a satisfaction level for each fuzzy goal and constraint.
In this study, we propose fuzzy goal programming with an S-shaped utility function as a decision aid to help homebuyers in choosing their preferred house via the Internet in an easy way. With the use of a decision aid, homebuyers can specify their housing goals and constraints with different priority levels and thresholds as a matching mechanism for a fuzzy search, while the matching mechanism can be trans-lated into a standard query language for a regular relational database. Moreover, a laboratory experiment is conducted on a real case to demonstrate the effectiveness of the proposed approach. The results indicate that the proposed method provides better customer satisfaction than manual systems in housing selection service.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
Many buyers’ experiences of using search tools through the Internet to find an appropriate house may not reduce their search time (D’Urso, 2002; Leonard, Ken, & Randy, 2003). This is due to the difficulty of evaluating the multitude of factors, such as emotional priorities, financial situations and arbitrary preferences at the same time. For the sake of easy illustration, we consider the following example throughout this paper. A young couple, Alice and John, decides to buy a house with emphasized consideration of chil-dren’s education. Alice would like to buy a house near the best high school in the city. In order to gather as much housing information as possible within the shortest time, Alice turns to the Internet. By using ‘‘real estate’’ as a keyword, she receives more than one million related links from Google. However, these real estate websites can only screen out houses that exactly match specific
constraints (e.g., city/state, price range and number of bedrooms) given by Alice. Alice is disappointed with the result because she cannot input appropriate criteria into the system to meet her needs, such as a house of ‘‘about’’ 250 square meters or ‘‘not too far’’ from her workplace. She scrutinizes the housing information listed on the Internet and eliminates the unqualified houses by herself. Since there are a huge number of alternatives, it is difficult for Alice to evaluate and rank them, and none of the online agents can provide a good ranking service.
How can someone become a successful real estate agent? They should provide an efficient and flexible search tool for homebuyers with different ages, housing considerations and risk attitudes. Usually, risk tolerance increases with age when other variables are controlled (Wang & Hanna, 1997). Young buyers, who have less money, may engage in less risk by selecting an apartment. Middle-aged buyers are risk lovers, with more money and more experience. Thus, they may choose bigger houses. With decreasing income, elders who are usually risk averters will choose houses with less risk such as countryside houses.
http://dx.doi.org/10.1016/j.ejor.2014.08.009
0377-2217/Ó 2014 Elsevier B.V. All rights reserved. ⇑Corresponding author.
E-mail address:chingter@mail.cgu.edu.tw(C.-T. Chang).
Contents lists available atScienceDirect
European Journal of Operational Research
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e j o rMost online real estate agents, such as Yahoo Real Estate (http://realestate.yahoo.com/) and Realtor.com (
http://www.real-tor.com/), provide a common search tool with basic constraints
for homebuyers to list all houses which exactly match their requirements from the database. In this case, some potential houses with slight deviations from the constraints will be excluded by using the search tool. That is, a good match between buyer and potential house is difficult to reach because everyone has his/her own preferences. With multiple housing goals and different prior-ities for each individual, comparing similar houses is very compli-cated work for agents. For example, a homebuyer would like to buy a suburban house with consideration of convenient transportation, beautiful environment and at least two bedrooms. However, so far, there is no online real estate agent providing appropriate tools to apply the functions of multi-goal and multi-criteria searches with fuzzy preferences.
2. Important concerns for online agents and homebuyers We list some important concerns for online agents and home-buyers as follows:
(1) There is a lot of fuzzy information on the Internet such as ‘‘great quiet neighborhood with excellent schools’’ or ‘‘close to world-class shopping, dining and entertainment at nearby Santana Row and Valley Fair Plaza’’.Liu and Zhang (2009) present a fuzzy evaluation method for residential real estate electronic marketing based on network DEA which uses
linguistic variables to evaluate the factors. However, thus far, online agents do not provide any appropriate search tool to aid buyers in describing their ambiguous criteria, such as ‘‘comfortable’’ environment and ‘‘nice’’ neighborhood for housing. Moreover, most of this information is considered as extra descriptions of houses and cannot be processed as a standard query search in a database system.
(2) Online real estate agents should provide a tool for homebu-yers to prioritize housing constraints. Customers also need a flexible method to determine the relative weights between constraints and rank housing alternatives. To increase the probability of finding the most suitable house, real estate agents should provide a better matching mechanism by tak-ing buyers’ preemptive priority preferences into account (Yuan, Lee, Kim, & Kim, 2013).
(3)Ford, Rutherford, and Yavas (2005)pointed out that online
homebuyers have to evaluate more houses in order to ulti-mately find a better match. This leads to higher transactional costs. Personalized service is an essential factor in increasing the competitiveness of online real estate agents (Hamilton &
Selen, 2004). However, tools of current agents do not
pro-vide the necessary personalization for housing evaluation and ranking. In reality, homebuyers need this service very much. Moreover, it is necessary to offer a user-friendly infor-mation search system so as to save busy customers’ time. (4) Online real estate agents should provide a tool to match
housing alternatives for buyers according to their housing philosophies and risk attitudes. With different risk attitudes, Table 1
Housing attributes.
Housing attributes Sub items of housing attributes Sources
Housing value Price Lindberg, Garling, & Montgomery (1989) and Michaelides (2011)
Owner’s estimate of annual housing value Arimah (1992)
Structure attributes Lot size Stull (1970), King (1976), and Lindberg et al. (1989)
Number of floors Arimah (1992)
Number of rooms Stull (1970), Arimah (1992)
Neighborhood attributes Pollution level Lindberg et al. (1989), Arimah (1992), Kim, Yang, Yeo, & Kim, 2005,
Natividade-Jesus et al. (2007)
Safety Kim et al. (2005)and Natividade-Jesus et al. (2007)
Landscaping Kim et al. (2005) and Waltert & Schlapfer (2010)
Recreational facilities in the neighborhood Lindberg et al. (1989) and Arimah (1992)
Location attributes Distance to Central Business District (CBD) Stull (1970), King (1976), Lindberg et al. (1989), Arimah (1992), and Natividade-Jesus et al. (2007)
Distance to workplace of head of household Lindberg et al. (1989) and Arimah (1992)
Average distance to children’s school Lindberg et al. (1989) and Arimah (1992)
Public transportation Kim et al. (2005)
*Lot size *Pollution level
*Landscaping *Safety *Distance to downtown *Price Level 1: Overall goal Level 2: Attributes Level 3: Sub-attributes
Housing Value Structure Neighborhood Location
Housing Selection *Owner's estimate of annual housing value *Number of floors *Number of rooms *Distance to workplace *Recreational facilities in the neighborhood *Average distance to children’s school *Public transportation Fig. 1. AHP hierarchy for housing selection.
buyers choose different houses according to the future value of a house (Zhang and Yang, 2012). Based on historical prices and utility functions, homebuyers can predict the future value of the house. This is another important function of the tool.
To the best of our knowledge, there is no single tool provided by current real estate agents to handle all the above-mentioned problems. Therefore, in this paper, we try to develop a decision support aid to quantify ambiguous search criteria and rank houses for buyers by considering the above factors. Such a system also allows customers to specify housing constraints with thresholds for standard fuzzy queries. All the constraints and fuzzy queries can then be translated into a series of precise queries for a regular relational database. Finally, in order to demonstrate the effective-ness of the proposed decision aid system, a laboratory experiment is conducted on a real case and detailed corresponding analysis is also provided.
3. Method and materials 3.1. Housing attributes classification
Bond, Seiler, Seiler, and Blake (2000)stated that the types of
online property information provided by most online real estate agents include geographic region, asked price, neighborhood, structural features and a picture of the house. Real-time listings and virtual home tours make real estate websites rich in content and help homebuyers to be better informed throughout the search and purchase process (Kummerow & Lun, 2005). Internet real estate agents, e.g., Yahoo Real Estate, Realtor.com, and Century 21 Real Estate (http://www.century21.com/home.aspx), usually allow homebuyers to specify characteristics of their target house such as the city, location, price range, number of bedrooms, and number of bathrooms. Then, homebuyers can receive a list of suggested houses based on their given constraints.
Obviously, these characteristics are important considerations for homebuyers. Because the Internet can increase search intensity, its prescreening capability allows homebuyers to discover and visit more appropriate properties in a short period (Zumpano, Johnson, & Anderson, 2003). However, the current searching functions pro-vided by online real estate agents seem too simple to meet buyers’ goals and preferences. In order to provide sufficient considerations for customers, this study collects important housing attributes from previous studies and interviews 10 house buyers and 10 senior real estate agents in Taiwan. Some duplicate or irrelevant attributes are eliminated and the selected list is depicted in Table 1.
In order to elicit important housing attributes for buyers, this study also constructs an Analytical Hierarchy Process (AHP)
(Saaty, 1980). AHP provides solutions for decision problems in
multi-criteria environments (Forman & Gass, 2001). This study constructs an AHP hierarchy of housing selection as shown in
Fig. 1. We invite twenty homebuyers to evaluate these housing
attributes using an AHP questionnaire which is partially listed in Appendix A. Finally, the overall relative weights of attributes and sub-attributes are obtained, as shown inTable 2. As seen, price is the most important factor. The second important consideration is the lot size. In addition, distance to children’s schools and safety are also important sub-attributes for housing choices.
In this paper, the Fuzzy Goal Programming (FGP) method with an S-shaped utility function is adopted to develop a decision sup-port system to help homebuyers search for appropriate houses on the Internet in consideration of their housing risk attitudes and satisfaction levels.
3.2. Data representation
The parameters which define the size of the problem are listed as follows:
x an n-vector with components x1, x2, . . ., xn
B the number of achieved fuzzy constraints
xi house alternatives, i = 1, . . ., n
Index sets:
k the kth goals
i the ith alternative
j the jth attribute
r the rth priority level, r = 1, 2, . . ., i 1 Problem data:
fk(x) the linear function of the kth goal
gk the aspiration level of the kth goal
lk lower limits for the kth goal
uk upper limits for the kth goal
Aij the jth attribute of the ith alternative
l
Aij utility function of the jth attribute and the ithalternative
l
Aij(x) the utility function of the decision maker’ssatisfaction level
l
attribute(AVj) the average satisfaction level for attribute jl
at least the utility functions of meeting the buyer’s ‘‘atleast’’ level constraints
l
at most the utility functions of meeting the buyer’s ‘‘atmost’’ level constraints
l
about Y the utility functions of meeting the buyer’s‘‘about’’ level constraints
Cr the binary variable for determining the
preemptive priority of the r-th fuzzy constraint
wks the weights attached to the bounded positive
deviations pksfor the sth break point in the kth
goal
pks the bounded positive deviations from the target
value bksfor the sth break point in the kth goal
bks the utility value of the break points in the kth
goal’s utility function
Sks the slope of the deviation between bks
kk the additional continuous variable that
represents the utility value in the kth goal eþ
k positive deviations from the highest possible
value of the utility function for the kth goal e
k negative deviations from the highest possible
value of the utility function for the kth goal
a
k the positive weights attached to the sum of thedeviations of kj k 1j
zk the linear function of the kth goal
l
ks(zk(x)) a membership function of the kth goalbk the positive weights obtained from AHP
attached to each goal
3.3. Goal programming and fuzzy goal programming
The housing choice, which involves homebuyers’ heteroge-neous preferences, is a typical multi-criteria and multi-objective decision-making problem. Buyers usually have different satisfac-tion levels for various housing criteria, such as the number of bed-rooms, quality of environment and convenience of transportation. Furthermore, they often expect some conflicting housing goals, such as minimizing house price while maximizing lot size and
location utility. In order to pursue aspirations-maximization,
Charnes and Cooper (1961)proposed Goal Programming (GP) to
model real world problems. GP is especially useful for multi-crite-ria and multi-objective decision problems. The mathematical for-mulation of GP is introduced as follows:
(GP)
Minimize X
m
k¼1
jfkðxÞ gkj ð1Þ
Subject to x 2 F; ðF is a feasible setÞ:
where fk(x) is the function of the kth goal and gkis the aspiration
level of the kth goal.
In order to resolve the imprecise aspiration level of the Decision maker’s (DM’s) goals,Narasinhan (1980)utilized the fuzzy weights approach to describe linguistic priorities in the utility functions. The conventional form of FGP can be expressed as follows:
(FGP)
fkðxÞ J gk ðorfkðxÞ K gkÞ k ¼ 1; 2; . . . n
Subject to x 2 F; ðF is a feasible setÞ ð2Þ
where fk(x) J ([gk) indicates the kth fuzzy goal approximately
greater or equal to (approximately less or equal to) the aspiration level gk; other variables are defined as in GP.
Fuzzy goals and fuzzy constraints can be defined as fuzzy sets in the space of alternatives (Bellman & Zadeh, 1970). This study adopts the fuzzy logic to deal with the linguistic words in fuzzy constraints, such as the safety of the house should be good. For the sake of simplicity, the preference-based utility functions are expressed as follows:
l
kðfkðxÞÞ ¼ 1; if fkðxÞ gk; ðfkðxÞlkÞ gklk ; if lk<fkðxÞ < gk for fkðxÞ J gk; 0; if fkðxÞ lk 8 > < > : ð3Þl
kðfkðxÞÞ ¼ 1; if fkðxÞ gk; ðukfkðxÞÞ ukgk ; if gk<fkðxÞ < uk for fkðxÞ K gk; 0; if fkðxÞ uk 8 > < > : ð4Þwhere lkand ukare, respectively, lower and upper limits for the kth
goal; fk(x) and gkare defined as in GP.
Online housing decision aids should not only consider the prior-ity weight of each goal but also the homebuyers’ fuzzy preferences. However, it is usually not easy to describe housing goals and crite-ria precisely. Housing decisions are laced with subjective human values that are usually neither crisp nor deterministic. In 2005,
Mohanty and Bhasker (2005) proposed a fuzzy approach for
solving production classification problems on the Internet. A DM usually searches for the best satisfactory product that fulfills
‘‘most’’ of the attributes rather than all attributes. Therefore, they defined the linguistic quantifier ‘‘most’’ as a key element for vague aspiration as follows:
l
mostðxÞ ¼ 1 x 0:8 ðx 0:3Þ=ð0:5Þ 0:3 x 0:8 0 x 0: 2 6 4 ð5ÞOther solutions include the weighted additive model, provided
byTiwari, Dharmar, and Rao (1987), and the weighted max–min
model, provided byLin (2004). However, with a preemptive prior-ity setting, unless a particular goal is achieved, other goals should not be considered. The inexperienced setting of weights in the formulation of GP can lead to incorrect results (Tamiz, Jones, & Romero, 1998).
Buckles and Petry (1983)developed a fuzzy relational model to
incorporate fuzzy information in a relational database. To extend database management systems functions for the expression of flexible queries,Bosc and Pivert (1995)introduced a SQLf language which is a fuzzy extension of standard query language (SQL).
Shenoi and Melton (1999)extended Buckles and Petry’s model to
incorporate with proximity relations for scalar domains. Yazici
and Cibiceli (1999) utilized a multi-dimensional data structure,
Multi Level Grid File, to access both crisp and fuzzy data from a fuzzy database.Ma and Yan (2007)presented generic fuzzy queries for a regular relationship database.
In order to handle DM’s fuzzy preferences,Fan, Ma, and Zhang
(2002) proposed a method to solve multiple attribute decision
making problems by considering the fuzzy relations of alternatives. Rasmy, Lee, Abd EI-Wahed, Ragab, and EI-Sherbiny (2002) established a fuzzy expert system based on the DM’s linguistic preferences for multiple objective decision making problems.
Cheng, Chan, and Lin (2006)derived a fuzzy inference system as
a negotiation agent to search for a mutually acceptable contract in an e-market.
Chang (2010)presented an approach to formulate an S-shaped
utility function without adding extra binary variables. The utility function describes the risk attitudes of DMs, including risk aversion and risk seeking. With different risk attitudes in gain or loss situations, homebuyers can find ideal houses with consideration of their housing preferences. In order to comprehend ambiguous housing goals and risk attitudes from with conflicting preferences, it is indispensable to determine the satisfaction level for each fuzzy goal and constraint.
There are several studies that integrated the AHP and GP (Badri, 2001; Ho, Chang, & Ku, 2013; Ramanathan & Ganesh, 1995;
Schniederjans & Garvin, 1997). Ramanathan and Ganesh (1995)
derived AHP weights for the qualitative criteria and employing them as coefficients of the decision variables in the objective Table 2
Composite priority weights for attributes and sub-attributes.
Attributes Local weights Sub-attributes Local weights Global weights Priority order
Housing value 0.23 Price 0.70 0.161 1
Owner’s estimate of annual housing value 0.30 0.069 8
Structure attributes 0.22 Lot size 0.50 0.110 2
Number of floors 0.10 0.022 13
Number of rooms 0.40 0.088 5
Neighborhood attributes 0.28 Pollution level 0.30 0.084 7
Safety 0.32 0.090 4
Landscaping 0.23 0.064 9
Recreational facilities in the neighborhood 0.15 0.042 11
Location attributes 0.27 Distance to downtown 0.16 0.043 10
Distance to workplace 0.32 0.086 6
Average distance to children’s school 0.40 0.108 3
functions of the GP model in solving energy resource allocation problem.Badri (2001)implemented the AHP weights for the qual-ity control instruments on each alternative as constraints in GP to reflect the preferences for the different instruments. Ho et al.
(2013)obtained weights from AHP and implement it upon each
corresponding goal using multi-choice goal programming for the location selection problem.
3.4. The proposed method
With prospect theory (Kahneman & Tversky, 1979), we can find the varying risk attitudes of DMs in different situations. DMs intend to avoid risk in choices involving sure gains and to seek risk in choices involving sure losses. Similarly, homebuyers exhibit more risk aversion in gain situations as a concave function. On the other hand, homebuyers prefer to be risk lovers in loss situa-tions as a convex function. Therefore, in uncertain situasitua-tions, each homebuyer should have his/her own S-shape utility function to represent at their risk attitudes.
The combination of the above mentioned function may lead to a more effective approach with many advantages. Moreover, it can solve some or all of the shortcomings of each individual approach. Therefore, we integrate FGP with an S-shaped utility function as a decision aid to help with Internet housing choices as follows.
This study formulates the buyer’s housing preference among alternatives with Eq.(6). There are K goals and each goal has with attributes Aij, (Aij,
l
Aij). The average satisfaction level for attribute jis given as
l
attributeðAVjÞ ¼ 1 K XK i¼1l
AijðxÞ ð6Þand the utility function of DM
l
Aij(x) is defined as in FGP.This study constructs the aspiration-maximization of the buyer’s housing goals in consideration of their risk attitudes (Eqs.
(7)–(11)) which are represented by the S-shaped utility function
(Chang, 2010), while the homebuyer’s preferences, such as price,
expected lot size and so on, are represented by Eq. (12). There are two housing goals about future value of the house, the maximi-zation of the expected gain and the minimimaximi-zation of the expected loss. With the slope increase/decrease, Eqs.(7)–(11)can formulate these two goals as a concave/convex function with homebuyers’ risk attitudes (risk averter/lover) in different situations. The approach described above leads to the following formulation:
Minimize bk ðwk1pk1þ wk2pk2þ wk3pk3þ
a
kðeþk þ ekÞÞ Subject to kk¼ ½l
ksðbk2Þl
ksðbk1Þ pk1 bk2 bk1 þ ½l
ksðbk3Þl
ksðbk2Þ pk2 bk3 bk2 þ ½l
ksðbk4Þl
ksðbk3Þ pk3 bk4 bk3 ; ð7Þ kk eþk þ ek ¼ 1; ð8Þ zkðxÞ pk1 pk2 pk3 bk1; ð9Þ wk1<wk2<wk3; ð10Þ 0 pk1 bk2 bk1; 0 pk2 bk3 bk2; 0 pk3 bk4 bk3; ð11Þl
AijðxÞl
attributeðAVjÞCr; r ¼ 1; 2; . . . m ð12Þ Xmr¼1
Cr B; ð13Þ
x 2 F ðF is a feasible setÞ
where bkare positive weights obtained from AHP attached to each
goal. With AHP method, the relative importance (the relative weights) between attributes will be translated as weights bk on
each corresponding goal in the FGP. wksare the weights attached
to positive deviations, pks(s = 1, 2, 3). pksare the positive deviations
from the target value bksfor the s th break point in the kth goal. kkis
the additional continuous variable that represents the utility value of the S-shaped utility function in Eq.(7). zk(x) is the linear function
of the kth goal. x is an n-vector with components x1, x2, . . ., xn.
l
ks(zk(x)) is a membership function of the kth goal. Cr(r = 1, 2, . . .,m) are binary variables for determining the preemptive priority of the rth fuzzy constraint. In the proposed model, a DM can choose different weights wks on each deviation to determine the priority
of deviations pks. The risk attitudes of DMs can be described as risk
averse (a concave utility function) and risk seeking (a convex utility function). In this study, we formulate these two housing risk attitudes in gain and loss situations as shown inFigs. 2–7.
Figs. 2 and 4present the concave utility function of a risk avert-er in gain and loss situations, respectively. As shown inFigs. 2 and 4, the slope decreases from |Sk1|, |Sk2| to |Sk3|. This means that with
the increased risk of expected gain/loss zk(x), the average
accumu-lated satisfaction level
l
ks(zk(x)) of the DM decreases. The slope|Si1| > |Si2| > |Si3| indicates that the DM is a risk averter. Figs. 3
and 5show a convex utility function of a risk lover in gain and loss situations, respectively. As seen inFigs. 3 and 5, the slope increases from |Sk1|, |Sk2| to |Sk3|. This means that with the increased risk of
expected gain/loss zk(x), the average accumulated satisfaction level
l
ks(zk(x)) of the DM increases. The slope |Sk1| < |Sk2| < |Sk3| showsthat the DM is a risk lover.
This study formulates homebuyers’ risk attitudes in gain situa-tions with an S-shaped utility function as shown inFig. 6. Where the average accumulated satisfaction level
l
ks(zk(x)) is a convexfunction (risk lover) for 0 6 zk(x) 6 ek and is a concave function
(risk averter) for zk(x) P ek. Similarly, the homebuyer’s two risk
attitudes in loss situations are formulated with an S-shaped utility function as shown inFig. 7, where the average accumulated satis-faction level
l
ks(zk(x)) is a concave function (risk averter) for0 6 zk(x) 6 ekand is a convex function (risk lover) for zk(x) P ek.
Sometimes, a homebuyer cannot find a suitable house when too many constraints are requested. For instance, he/she may set many constraints such as distance to a market and distance to the nearest major hospital at the same time. He/she may find no house meeting these criteria due to excessive specificity. In contrast, if a preemptive priority is set for each constraint or the relationship between constraints is determined, the suitable house could be found more easily from their criteria, and the probability of finding a satisfactory house would increase. The preemptive priority struc-ture can be stated as CroCr+meaning that the constraint in the rth evaluation criteria has higher priority than the (r + 1)-th evaluation criteria. With Eqs.(12) and (13), a homebuyer can set a preemptive priority for each constraint to obtain the best
available housing options. This modified FGP can determine the most appropriate constraints and recommend a suitable ranking list. In contract, for classic FGP methods, setting relationships among each constraint would be almost impossible.
Let us consider a simple modified FGP example with preemp-tive priority to demonstrate the above-mentioned idea. A homebu-yer, Alice, sets three constraints in Eqs.(14)–(16)as: (i) the safety should be good at least so and so, (ii) the pollution level should be low at least so and so, and (iii) the view should be good at least so and so, and specifies that only one of these needs should be achieved. The problem can be formulated as the following achieve-ment function.
Minimize wk1pk1þ wk2pk2þ wk3pk3þ
a
kðeþk þ e kÞSubject to
l
AijðxÞl
safetyðAVjÞC1 ð14Þl
AijðxÞl
pollutionðAVjÞC2 ð15Þl
AijðxÞl
viewðAVjÞC3 ð16ÞC1þ C2þ C3¼ 1 ð17Þ
where xi(i = 1, . . ., 9) and Cr(r = 1, 2, 3) are binary variables
Because Crðr ¼ 1; 2; 3Þ are binary variables, thus, Eq. (17)
dictates that only one constraint is fulfilled in Eqs. (14)–(16). Accordingly, Alice can set different preemptive weights for her constraints according to her preferences.
In order to implement the fuzzy concept, this study combines FGP and homebuyer’s fuzzy constraints with linguistic quantifiers, such as ‘‘at least’’, ‘‘at most’’ or ‘‘about’’. For example, we replace
l
attribute(AVj) withl
atleast(q) in Eq.(18) to meet the homebuyer’sconstraints with ‘‘at least’’ Other utility functions of the fuzzy constraints such as ‘‘at least Y’’, ‘‘at most Y’’ and ‘‘about Y’’ are defined as in the model proposed byMa and Yan (2007).
l
atleastðqÞ ¼ 0; if q a; ðqaÞ Ya; if a < q < Y; 1; if q Y 8 > < > : ð18Þl
at mostðqÞ ¼ 1; ðbqÞ bY ; if Y < q < b 0; 8 > < > : ð19Þl
about YðqÞ ¼ 1 1 þ qY b 2; ð20ÞFig. 3. A convex utility function as a risk lover in gain situation.
Fig. 4. A concave utility function as a risk averter in loss situation.
Fig. 5. A convex utility function as a risk lover in loss situation.
Fig. 6. A right S-shaped utility function represents risk attitudes in gain situation.
where larger values of b correspond to a wide curve and a and b are, respectively, lower and upper limits for each fuzzy constraint.
DMs can determine the housing constraints with different thresholds for fuzzy queries, and then these fuzzy queries are translated into precise SQL for a regular relational database as follows.
SELECT housing alternative FROM housing table WHERE Attribute at least=
most WITH matching rateðfuzzy queryÞ ð21Þ
Fuzzy query Eq.(21)can be substituted by precise query Eq.(22) when implemented in the relational database.
WHERE A a AND A bðprecise queryÞ ð22Þ
In short, the main contributions of the proposed method are as follows.
1. Homebuyers can easily describe and quantify ambiguous housing preferences with fuzzy satisfaction levels. More-over, online real estate agents can even convert this approach into a utility function.
2. DMs can decide suitable weights for their risk attitudes in different situations. To express the risk attitudes in differ-ent situations, they assign differdiffer-ent expected gains or losses on individual house alternatives. The proposed approach can transform these risk attitudes into weights for each target and present different housing ranks. 3. DMs can set preemptive priorities for each constraint
according to different situations and obtain different hous-ing ranks which are closer to their preferences.
4. The proposed approach can deal with fuzzy searches in related databases on the Internet for buyers. In order to meet their constraints with linguistic quantifiers, this model evaluates the houses by giving preferential weights according to these fuzzy satisfaction levels.
The approach involves inputting the homebuyer’s preferences, goals and criteria, and developing a modified FGP model to obtain individual solutions for each objective function as in the following six steps: Step 1: Identify the homebuyer’s housing goals with suit-able risk attitude and roughly determine his/her housing criteria. Step 2: Define the homebuyer’s satisfaction level for each housing goal and criterion. This process allows a homebuyer to develop their own utility function for the fuzzy goals and ambiguous crite-ria. Step 3: Search for possible alternatives in the database on the Internet using linguistic quantifiers such as ‘‘at least’’, ‘‘at most’’ or ‘‘about.’’ Step 4: Establish the FGP model with an S-shaped utility function, and aggregate all the homebuyer’s fuzzy goals and crite-ria. Step 5: Solve the FGP model with an S-shaped utility function, which evaluates each alternative according to the homebuyers’ risk attitude and the scoring attribute set by the fuzzy preferences. Step 6: Rank the house alternatives based on obtained scores, with which the customer can finally choose the utility-maximizing house. 4. Results and discussion
4.1. An illustrative real case
A real case is presented to illustrate how a personalized ranking method can create more accurate list of ideal houses for homebu-yers. Alice, who works for a computer company in San Jose, would like to buy a house for her family. Considering her children’s edu-cation, she would prefer a house located in a neighborhood with good high schools – Monta Vista High School, Gunn High School or San Jose High Academy. In addition to location, price is her
second most important concern. Based on these considerations, Alice offers her housing goals and criteria to Google to search for suitable houses. However, the searching results are quite frustrat-ing because she obtains too many alternatives. She has to expend a lot of time to screen the alternatives. The current tools of online agents only provide explicit inputs that cannot deal with buyers’ fuzzy priorities. Moreover, most of online real estate agents do not provide a landmark searching choice. This makes it even more difficult for Alice to find an appropriate house in a desired location. The proposed method can solve the above-mentioned problems and exclude most unacceptable alternatives. Furthermore, it also creates a personalized ranking list according to the scoring attributes of her fuzzy preferences. The interface of this housing decision aid is presented inFig. 8. The proposed system can consider multiple constraints in regard to the ‘‘distance of the house to some places’’. InFig. 8, the real-time fuzzy utility functions are provided to help homebuyers estimate their preferences more accurately.
First, Alice gets the relative weights with the AHP questionnaire. The overall relative weights of attributes and sub-attributes are obtained, as shown inTable 3.
From the result of AHP inTable 3, we can find Alice’s top two important attributes are Owner’s estimate of annual housing value and Lot size. Therefore, Alice selects three housing goals (G1, G2, G3, K = 3) about the potential gain, the potential loss and the lot size of a house. The objective is to find houses closest to her preferences. The satisfaction levels for each goal are expressed by an S-shaped utility function as shown inFigs. 9–11. The expected gains and losses of twenty house alternatives (n = 20) are listed inTable 4.
(G1) The potential gain should be over 20 thousand dollars and the more the better.
According to the prospect theory (Kahneman & Tversky, 1979), a DM will be more risk averse in a gain situation. Vise versa, in a loss situation, a DM will be more risk seeking. We interview Alice and formulate the satisfaction level of her expected gain for houses as shown inFig. 9. Obviously, she is a risk lover when the expected gain is lower than 45 thousand dollars (as a convex function) and a risk averter when the expected gain is more than 45 thousand dol-lars (as a concave function) in a gain situation. The spot line indi-cates that the turning point of 45 thousand dollars separates the convex and concave function inFig. 9. The bold line indicates the right S-shaped utility function which is established by both convex and concave function.
Based on Alice’s requirements, the problem can be formulated as follows. In this illustrative case, we set
a
k= 7000, a relative largenumber, in order to increase the influence of ðeþ kþ ekÞ. Minimize p11þ 2p12þ 3p13þ 4p14þ 5p15þ 7000ðeþ1þ e 1Þ Subject to k1¼ ½0:15 0 p11 30 5þ ½0:3 0:15 p12 40 30 þ ½0:6 0:3 p13 50 40 þ ½0:8 0:6 p14 65 50 þ ½1 0:8 p15 100 65; k1 e þ 1þ e1 ¼ 1; z1ðxÞ p11 p12 p13 p14 p15¼ 5; X20 i¼1 xi¼ 1; 0 p11 30 5; 0 p12 40 30; 0 p13 50 40; 0 p14 65 50; 0 p15 100 65; z1ðxÞ ¼ 100x1þ 80x2þ 70x3þ 60x4þ 55x5þ 40x6 þ 50x7þ 45x8þ 50x9þ 90x10 þ 85x11þ 70x12þ 20x13þ 35x14þ 30x15 þ 40x16þ 25x17þ 20x18þ 10x19þ 5x20;
This problem is solved by using LINGO (Schrage, 2002) to obtain the solution as (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20) = (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0), (p11, p12, p13, p14, p15) = (25, 10, 10, 15, 35) and the utility value
k¼ 1 (i.e., the rate of homebuyer satisfaction is 100%). The recommended alternative is house x1and the expected gain of this
house is 100 thousand dollars.
Fig. 8. The interface of the housing decision aid - satisfaction level setting.
Table 3
Composite priority weights for attributes and sub-attribute from Alice.
Attributes Local weights Sub-attributes Local weights Global weights Priority order
Housing value 0.32 Price 0.4 0.128 3
Owner’s estimate of annual housing value 0.6 0.192 1
Structure attributes 0.28 Lot size 0.55 0.154 2
Number of floors 0.15 0.042 10
Number of rooms 0.3 0.084 5
Neighborhood attributes 0.26 Pollution level 0.21 0.0546 8
Safety 0.33 0.0858 4
Landscaping 0.32 0.0832 6
Recreational facilities in the neighborhood 0.14 0.0364 11
Location attributes 0.14 Distance to downtown 0.14 0.0196 12
Distance to workplace 0.42 0.0588 7
Average distance to children’s school 0.33 0.0462 9
Public transportation 0.11 0.0154 13
Note: The bold values inTable 3are the top two highest values among all global weights.
convex function
concave function
Rate of homebuyer satisfaction
1.0 0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 10 Expected gain (thousand dollars) 20 30 40 50 60 70 80 90 100 110 120 5
Fig. 9. Alice’s right S-shaped utility function in gain situation.
Table 4
The expected gain and loss of the twenty house alternatives. House alternatives Expected gain (thousand dollars) Expected loss (thousand dollars) x1 100 80 x2 80 50 x3 70 50 x4 60 40 x5 55 30 x6 40 45 x7 50 55 x8 45 90 x9 50 45 x10 90 20 x11 85 20 x12 70 30 x13 20 40 x14 35 30 x15 30 45 x16 40 40 x17 25 10 x18 20 20 x19 10 10 x20 5 5
(G2) The potential loss should not be over 100 thousand dollars and the less the better.
In a loss situation, Alice becomes more risk seeking. Assume that the satisfaction level of her expected loss is shown in
Fig. 10. As seen, she is a risk averter when the expected loss of
the house is lower than 50 thousand dollars (a concave function) and a risk lover when the expected loss of the house is more than 50 thousand dollars (a convex function). InFig. 10, the spot line indicates that the turning point of 50 thousand dollars separates the convex and concave functions. The bold line indicates the left S-shaped utility function is established by both convex and concave functions.
This case can be expressed as follows:
Minimize 4p21þ 3p22þ 2p23þ p24þ 7000ðeþ2þ e2Þ Subject to k2¼ 1 ð½1 0:8 p21 30 0þ ½0:8 0:4 p22 50 30 þ ½0:4 0:13 p23 90 50þ ½0:13 0 p24 128 90Þ; k2 eþ2þ e 2¼ 1; z2ðxÞ p21 p22 p23 p24 0; X20 i¼1 xi¼ 1; 0 p21 30 0; 0 p22 50 30; 0 p23 90 50; 0 p24 128 90; z2ðxÞ ¼ 80x1þ 50x2þ 50x3þ 40x4þ 30x5 þ 45x6þ 55x7þ 90x8þ 45x9þ 20x10 þ 20x11þ 30x12þ 40x13þ 30x14þ 45x15 þ 40x16þ 10x17þ 20x18þ 10x19þ 5x20;
This problem is solved by using LINGO (Schrage, 2002) to obtain the solution as (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16,
x17, x18, x19, x20) = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1),
(p21, p22, p23, p24) = (0, 0, 0, 5) and the utility value k2¼ 0:9829 (i.e.,
the rate of homebuyer satisfaction is 98.29%). The recommended alternative is house x20. The expected gain of this house is 5
thou-sand dollars and the expected loss is also 5 thouthou-sand dollars. (G3) The lot size should be around 1000 square meters and must be over 700 but not over 1500 with the more the better. Alice does not want to buy too big of a house because of the cost and time needed for maintenance. Hence, the satisfaction level reaches 0 if the lot size is over 1500. In this case, the house size utility func-tion can be expressed as a concave funcfunc-tion inFig. 11.
This problem is formulated inAppendix B(the part of G3) and is solved by using LINGO (Schrage, 2002) to obtain the solution as (x1,
x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19,
x20) = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (p31, p32,
p33) = (50, 100, 300) and the utility value k3¼ 1 (i.e., the rate of
homebuyer satisfaction is 100%). The recommended alternative is house x2. The expected gain of this house is 80 thousand dollars,
the expected loss is 50 thousand dollars and the lot size is 1249 square meters.
Considering three goals of expected gain and loss simulta-neously and also the lot size, we formulate this problem in the
appendix Bagain and it is solved by using LINGO (Schrage, 2002)
to obtain the solution as (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12,
x13, x14, x15, x16, x17, x18, x19, x20) = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0), (p11, p12, p13, p14, p15, p21, p22, p23, p24, p31, p32,
p33) = (25, 10, 10, 15, 15, 0, 0, 12, 38, 50, 100, 300) with the utility
values k1¼ 0:8857, k2¼ 0:789 and k3¼ 1. The recommended
alternative is house x2. The expected gain of x2 is 80 thousand
dollars, the expected loss is 50 thousand dollars and the lot size of the house is 1249 square meters.
Comparison of the results in the above four situations is shown inTable 5. If we consider the potential gain (G1) alone, house x1,
which has the highest expected gain is the best choice. If we con-sider the potential loss (G2) alone, house x20, which has the lowest
expected loss, is selected. If we consider the lot size (G3) alone, house x2, which has the largest lot size, is the best choice. However,
if we consider the three goals, potential gain, loss and lot size, simultaneously, house x2, which has relatively high expected gain,
low loss and largest lot size is the best choice. In this case, the rate of homebuyer satisfaction for lot size (G3) is the highest utility value among the three goals. The rates of homebuyer satisfaction for the potential gain (G1) and for the potential loss (G2) decrease. This may be because the houses with big lot size also have relatively high potential loss.
(Constraints).
In order to better suit the real world, seven constraints are spec-ified as follows. For general constraints, the price, number of bed-rooms, distance from house to work, and the reliability of house information must be achieved. As for environmental constraints, safety, pollution level and view are considered. At least two of these constraints should be satisfied. The preferences for each con-straint are expressed inTable 6. (1) The house price should be around 300 thousand dollars but should not exceed 600 thousand dollars. If the house price is lower than 100 thousand dollars which is far under the market price, Alice thinks it may have a quality issue. (2) The safety of the house should at least be good. (3) The pollution level should be low at least. (4) The view from the house should be good at least. (5) There must be at least 2 bedrooms, and 4 bedrooms are desired. (6) The distance from house to work is not too far and at most 13 miles. (7) The reliability of house information should at least be average.
Alice would like to find the qualified houses that at least reach her housing constraints at different levels with thresholds for the fuzzy queries. Hence, we use the utility function approach to trans-late the fuzzy range with linguistic quantifiers into a crisp range as shown in Table 7. With different matching rates for each
convex function concave function 1.0 0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Rate of homebuyer satisfaction
10
Expected loss (thousand dollars) 40
20 30 50 60 70 80 90 100 110 120
Fig. 10. Alice’s left S-shaped utility function in loss situation.
concave function
Rate of homebuyer satisfaction
1.0 0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 60 Lot Size
(ten square meters)
70 80 90 100 110 120 130 140 150
constraint, the search results provide twenty available houses from the Yahoo Real Estate database as shown inFig. 12. The housing parameters and satisfaction levels of these twenty houses are listed
inTable 8. It is of note that the distance from house to work is
calculated by using Google Maps (http://maps.google.com/). Also, Alice can get the distances from available houses to a specific point from Google Maps and then input the data into the proposed decision support system to find appropriate houses.
To calculate the average satisfaction level for each attribute of the houses with Eq. (6), we have AVroom= 0.835, AVwork= 0.815,
AVview= 0.83. According to Alice’s preferences, the real estate agent
evaluates the available houses by assigning weights to maximize her expected satisfaction with three goals subject to all constraints. This problem is formulated in theAppendix B. The relative weights obtained from AHP inTable 3are attached on each corresponding goal in the FGP as follows.
Minimize 0:192 ðp11þ 2p12þ 3p13þ 4p14þ 5p15þ 7000ðeþ1 þ e 1ÞÞ þ 0:192 ð4p21þ 3p22þ 2p23þ 1p24þ 7000ðeþ2þ e 2ÞÞ þ 0:154ðp31þ 2p32þ 3p33þ 7000ðeþ3þ e3ÞÞ
From Table 3, the weight value of owner’s estimate of annual
housing is 0.192 which is attached on G1 and G2. Also, the weight value of lot size is 0.154 which is attached on G3.
The problem is solved by using LINGO (Schrage, 2002) to obtain the solution as (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20) = (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0), (p11, p12, p13, p14, p15, p21, p22, p23, p24, p31, p32, p33) = (20, 10, 10,
15, 0, 0, 0, 2, 38, 50, 100, 145). As seen, G1 = 60
(5 + 20 + 10 + 10 + 15 = 60) can be observed fromFig. 9, i.e., Alice’s expected gain is 60 thousand dollars for the new house, x4, with
the utility value k1¼ 0:77. G2 = 40 (0 + 0 + 2 + 38 = 40) can be
observed fromFig. 10, i.e., Alice’s expected loss is 40 thousand dol-lars for the new house, x4, with the utility value k2¼ 0:8565.
G3 = 1094 (700 + 50 + 100 + 145 + 99 = 1094) can be observed from Fig. 11, i.e., the lot size is 1094 square meters with the utility value k3¼ 0:7933. House x4with the relative high expected gain and low
loss is the best choice for Alice. The rates of homebuyer satisfaction for all three goals are above 77%.
In order to discover more suitable houses, Alice adjusts different preemptive priorities on constraints 2–6 with Eq.(12)and then the best alternative is derived accordingly inTable 9. FromTable 9, houses x2, x4 and x10 are the three best choices for Alice. If she
determines that some of constraints 1–3 (safety, pollution level and view) should be achieved, house x10, which has very good
safety, an average pollution level and a good view, would be the best choice. However, when constraints 1–3 are all need to be achieved, the best choice becomes house x2, which has good safety,
a low pollution level and a very good view. When all five Table 6
Alice’s housing constraints and the satisfaction level for each constraint. Price (thousand dollars) Satisfaction level Safety Satisfaction level l Pollution level Satisfaction level l View Satisfaction level l Number of bedrooms Satisfaction level The distance from house to work (mile) Satisfaction level The reliability of house information Satisfaction level 100 0 Very good
1 Very high 0 Very
good
1 1 0 4 1 Very good 1
200 0.8 Good 0.8 High 0.4 Good 0.9 2 0.8 5 0.9 Good 0.9
300 1 Average 0.6 Average 0.7 Average 0.7 3 0.9 13 0.8 Average 0.7
400 0.6 Bad 0.4 Low 0.9 Bad 0.4 4 1 15 0.5 Bad 0.4
500 0.3 Very
bad
0 Very low 1 Very
bad
0 5 1 20 0.3 Very bad 0
Table 5
The comparison of the results in four situations.
P11 P12 P13 P14 P15 P21 P22 P23 P24 P31 P32 P33 The selected house k1 k2 k3 Expected gain (thousand dollars) Expected loss (thousand dollars) Lot size (square meters) Goal 1 25 10 10 15 35 x1 1 100 80 798 Goal 2 0 0 0 5 x20 0.9829 5 5 850 Goal 3 50 100 300 x2 1 80 50 1249 Goals 1–3 25 10 10 15 15 0 0 12 38 50 100 300 x2 0.8857 0.7890 1 80 50 1249 Table 7
Translation of fuzzy range into crisp range of housing constraints.
Constraints Fuzzy range of housing constraints Crisp range of housing constraints
Constraint 2: Safety The safety should at least be good The description of the house should include the word ‘‘safety’’, and the satisfaction level of ‘‘the safety of the house’’ should at least be 80%
Constraint 3: Pollution level The pollution level should at least be low The description of the house should not include the word ‘‘pollution’’, and the satisfaction level of ‘‘the pollution of the house’’ should at be least 90%
Constraint 4: View The view should at least be good The description of the house should include the word ‘‘view’’, and the satisfaction level of ‘‘the view of the house’’ should at least be 90%
Constraint 5: Number of bedrooms
There must be at least 2 bedrooms, and 4 bedrooms will be good
There must be at least 2 bedrooms, and the satisfaction level of ‘‘the number of bedrooms’’ should at least be 80%
Constraint 6: The distance from the house to the workplace
The distance from the house to the workplace is ‘‘not too far’’ and at most 13 mile
The distance from the house to the workplace do not exceed 13 mile and the satisfaction level of ‘‘The distance from the house to the workplace’’ should at least be 84% Constraint 7: The reliability of
the house information
The reliability of the house information should at least be average
The description of the house should make the homebuyer feel reasonable, and the satisfaction level of ‘‘the reliability of the house information’’ should at least be 70%
constraints need to be satisfied, house x4is chosen because it has
low-price, a low-pollution level and is near her workplace. In this way, Alice can easily find a better house ranking list cho-sen according to her personal preferences and constraints. The pro-posed method can also provide a better suggestion for homebuyers and increase the probability of making a good decision when searching on the Internet.
4.2. A laboratory experiment
In order to investigate the customer satisfaction of the proposed decision aid system, a laboratory quasi-experiment has been
implemented using Active Server Pages and an Access database. The interface of the decision aid system is presented inFig. 8. We adopt (Pereira’s, 1999) questionnaire and use the modified research model as shown inFig. 13. The experimental subjects are 250 middle-aged workers with house-buying experience in central Taiwan. They have used the Internet to search for housing information or buy houses. 125 subjects are instructed not to use the housing decision aid and the other 125 subjects use this sys-tem. Subjects are approximately distributed equally by gender and age. All subjects input their preferred price range and zip code. Then our decision aid system presents housing suggestions. Sub-jects without access to the housing decision aid have to decide Fig. 12. Twenty house alternatives (http://realestate.yahoo.com/California/San_Jose/Homes_for_sale/result.html).
Table 8
House parameters and the satisfaction levels of 20 alternatives. House
alternatives
Price lprice Lot Size (square meters)
Safety lsafetyPollution level
lpollution View lview Number of bedrooms lroom Distance to the workplace (mile) lwork Reliability of the house information lreliability
x1 $330,000 0.88 798 Very Good 1 Average 0.7 Good 0.9 2 0.8 10.4 0.833 Good 0.9
x2 $320,000 0.92 1249 Good 0.8 Low 0.9 Very Good 1 3 0.9 10.1 0.836 Very good 1
x3 $316,000 0.94 1148 Very Good 1 Low 0.9 Average 0.7 2 0.8 9.7 0.841 Average 0.7
x4 $307,000 0.972 1094 Good 0.8 Low 0.9 Good 0.9 3 0.9 6.2 0.885 Average 0.7
x5 $295,000 0.99 871 Good 0.8 Low 0.9 Good 0.9 2 0.8 11.4 0.82 Good 0.9
x6 $285,000 0.97 924 Average 0.6 Low 0.9 Average 0.7 2 0.8 12.9 0.813 Average 0.7
x7 $275,000 0.95 997 Very Good 1 Low 0.9 Good 0.9 2 0.8 12.1 0.811 Good 0.9
x8 $262,888 0.926 770 Bad 0.4 Average 0.7 Very Good 1 2 0.8 5.4 0.895 Very good 1
x9 $249,950 0.9 903 Good 0.8 High 0.4 Bad 0.4 2 0.8 10.8 0.828 Bad 0.4
x10 $275,000 0.95 990 Very Good 1 Average 0.7 Good 0.9 2 0.8 6.2 0.885 Good 0.9
x11 $300,000 1 950 Good 0.8 Low 0.9 Average 0.7 3 0.9 9.7 0.841 Very good 1
x12 $250,000 0.9 850 Good 0.8 Low 0.9 Good 0.9 2 0.8 5.4 0.895 Average 0.7
x13 $263,000 0.926 800 Good 0.8 Average 0.7 Average 0.7 3 0.9 10.1 0.836 Average 0.7
x14 $316,000 0.94 1100 Good 0.8 Low 0.9 Average 0.7 3 0.9 11.4 0.82 Good 0.9
x15 $300,000 1 900 Good 0.8 Low 0.9 Average 0.7 2 0.8 12.9 0.813 Very good 1
x16 $307,000 0.972 1000 Good 0.8 Average 0.7 Good 0.9 3 0.9 5.4 0.895 Average 0.7
x17 $250,000 0.9 840 Good 0.8 Low 0.9 Average 0.7 2 0.8 10.8 0.828 Average 0.7
x18 $250,000 0.9 850 Very Good 1 Low 0.9 Very Good 1 3 0.9 13 0.8 Very good 1
x19 $200,000 0.8 800 Good 0.8 Low 0.9 Average 0.7 2 0.8 20 0.3 Good 0.9
which house is the best choice for them. Subjects with access to the decision aid system have to identify the housing goals with risk attitude and define their satisfaction level for each goal and
criterion with an S-shaped utility function. Then our system calcu-lates and aggregates all of the subject’s fuzzy housing goals and cri-teria using the FGP model. Finally, the rank of house alternatives is derived.Table 10illustrates the values of Cronbach’s
a
for the used measures indicating that the measures have high reliability.A single factor Analysis of variance (ANOVA) test is conducted to examine the influence of the variable ‘‘Housing decision aid’’ on mediating and dependent variables. The factor ‘‘Housing deci-sion aid’’ is coded as a dummy variable, i.e., present or absent. The constructs Effort, Savings and Satisfaction are represented as the mean-centered scores on a seven-point Likert scale. The system calculates a similarity score, with a range from 0 (completely dif-ferent) to 100 (completely similar) for each alternative based on the fuzzy queries and preferences of the DM. The results of the experiment are listed inTables 11 and 12. The ‘‘Housing decision aid’’ variable has a significant influence on the satisfaction variable. The mean value of Satisfaction for users with access to the decision aid system (4.638) is higher than that for those with no access to the decision aid system (3.712). This indicates that use of the hous-ing decision aid significantly increases the satisfaction levels of customers. The single factor ANOVA test of the influence of the housing decision aid on Satisfaction shows a significant relation-ship (F = 3.746; p < 0.05).
Furthermore, a single factor ANOVA test is performed with regression analysis of Satisfaction related to Effort, Savings and Similarity. We find a significant explanation of variation for Satis-faction in Table 11. Savings (b = 0.386; t = 4.424), Similarity (b = 0.328; t = 3.315) and Effort (b = 0.204; t = 3.142) have sig-nificant influence on Satisfaction.
After conducting the laboratory experiment, we have found some challenges for our housing decision aid. First, subjects some-times obtain too many or too few alternatives from the decision aid system because of restricted criteria. Fortunately, this aid can rank the house alternatives according to the aggregation of the buyer’s fuzzy goals and criteria using the FGP model. The ranking list helps subjects avoid confusion about similar houses. Second, it is not easy for customers to identify their housing goals with suitable risk attitude and determine the expected gain and loss of alternatives. The proposed decision aid can collect recent prices of houses which Access to the housing decision aid Cognitive decision effort Satisfaction with the decision process + the alternatives in Similarity among +
consideration set
-
-+ +
Perceived cost savings
Fig. 13. Influence of housing decision aid on satisfaction with the decision process.
Table 10
Reliability of the used measures.
Construct Measure Cronbach’sa
Effort Cognitive decision effort 0.87
Similarity Similarity among the alternatives in consideration set
0.83
Savings Perceived cost savings 0.88
Satisfaction Satisfaction with the decision process 0.84 Housing
decision aid
Access to the housing decision aid
Table 11
Result of single factor ANOVA tests. Dependent variable Mean of samples with access to decision aid Mean of samples without access to decision aid F Significance level Effort 3.12 3.38 9.324 0.012** Similarity 82.24 70.28 12.018 0.001** Savings 4.46 3.42 3.125 0.026** Satisfaction 4.638 3.712 3.746 0.024**
** Significance at the 0.05 level of significance (p < 0.05).
Table 12
Result of regression analysis. Dependent variable R Square Adjusted R square F-Statistic significance level
bCoefficient for effort t-statistic significance level
bCoefficient for similarity t-statistic significance level
bCoefficient for savings t-statistic significance level
Satisfaction 0.412 0.322** F
3,50= 9.455 b= 0.204 b= 0.328 b= 0.386
0.001** t = 3.142 t = 3.315 t = 4.424
0.0012** 0.026** 0.004**
** Significance at the 0.05 level of significance (p < 0.05). Table 9
Different preemptive priorities on each constraint and the derived best house.
Constraints Constraint 2: Safety Constraint 3: Pollution level Constraint 4: View Constraint 5: Number of bedrooms
Constraint 6: Distance to the workplace The best house C1 C2 C3 C4 C5 C1+ C2+ C3P1, C4+ C5= 0 1 0 0 0 0 x10 C1+ C2+ C3P1, C4+ C5= 1 1 0 0 1 0 x10 C1+ C2+ C3P1, C4+ C5= 2 1 0 0 1 1 x10 C1+ C2+ C3P2, C4+ C5= 0 1 0 1 0 0 x10 C1+ C2+ C3P2, C4+ C5= 1 1 0 1 1 0 x10 C1+ C2+ C3P2, C4+ C5= 2 1 0 1 1 1 x10 C1+ C2+ C3P3, C4+ C5= 0 1 1 1 0 0 x2 C1+ C2+ C3P3, C4+ C5= 1 1 1 1 1 0 x2 C1+ C2+ C3P3, C4+ C5= 2 1 1 1 1 1 x4
are similar to the alternatives in order to determine the expected gain and loss. During the searching procedure, homebuyers usually spend 20–30 min on the traditional real estate site, Yahoo Real Estate, to find desired houses. However, it only takes 8–10 min for customers using our housing decision aid to obtain target houses. It is clear that the proposed decision aid system is more efficient than traditional search tools.
5. Conclusions
Creating an online search tool with a user-friendly interface for house searches is the key success factor for winning consumers’ trust and preference. Nevertheless, current online agents cannot provide powerful search tools to meet homebuyers’ possible con-flicting goals and heterogeneous preferences. This study presents an integrated approach to support homebuyers in their online evaluation process. The proposed approach screens available houses according to homebuyers’ risk attitudes in loss or gain sit-uations. In this way, the proposed approach maximizes the sum of satisfaction levels with given weighted goals. Available houses with some important advantages but slight deviations from the search specifications are not retrieved by current systems. This issue can be solved by the proposed decision aid system. Also, DMs can determine the appropriate constraints with different thresholds for fuzzy queries. In order to meet the buyer’s con-straints with linguistic quantifiers, this method evaluates available houses by translating the DM’s queries into precise SQL queries.
The proposed approach transforms homebuyers’ fuzzy satisfac-tion levels into a fixed form. Then the ranking results of houses can be created for homebuyers. Personalized ranking is provided by the proposed system. Homebuyers can adjust their fuzzy goals or set different preemptive priorities on each constraint with ease to derive the different ranking lists. This can help buyers clarify their thoughts about the ideal house. A good ranking list can dramati-cally reduce search time and increase the matching rate.
In the competitive market of real estate, it is important to pro-vide a user-friendly interface for customers to input fuzzy criteria and then derive a ranking list based on buyers’ preferences and risk attitudes. This study finds that customer satisfaction is signifi-cantly increased by the use of the proposed housing decision aid. Appendix A. AHP questionnaire
Appendix B. Model formulation
Minimize 0:192 ðp11þ 2p12þ 3p13þ 4p14þ 5p15þ 7000ðeþ1þ e1ÞÞ þ 0:192 ð4p21þ 3p22þ 2p23þ 1p24þ 7000ðeþ2þ e2ÞÞ þ 0:154 ðp31þ 2p32þ 3p33þ 7000ðeþ3þ e3ÞÞ Subject to k1¼ ½0:15 0 p11 30 5þ ½0:3 0:15 p12 40 30 þ ½0:6 0:3 p13 50 40 þ ½0:8 0:6 p14 65 50þ ½1 0:8 p15 100 65; ðfor G1Þ k1 eþ1þ e1¼ 1; z1ðxÞ p11 p12 p13 p14 p15¼ 5; 0 p11 30 5; 0 p12 40 30; 0 p13 50 40; 0 p14 65 50; 0 p15 100 65; z1ðxÞ ¼ 100x1þ 80x2þ 70x3þ 60x4þ 55x5þ 40x6 þ 50x7þ 45x8þ 50x9þ 90x10 þ 85x11þ 70x12þ 20x13þ 35x14þ 30x15þ 40x16 þ 25x17þ 20x18þ 10x19þ 5x20; k2¼ 1 ½1 0:8 p21 30 0þ ½0:8 0:4 p22 50 30 þ½0:4 0:13 p23 90 50þ ½0:13 0 p24 128 90 ;ðfor G2Þ k2 eþ2þ e2¼ 1; z2ðxÞ p21 p22 p23 p24 0; 0 p21 30 0; 0 p22 50 30; 0 p23 90 50; 0 p24 128 90; z2ðxÞ ¼ 80x1þ 50x2þ 50x3þ 40x4þ 30x5þ 45x6 þ 55x7þ 90x8þ 45x9þ 20x10 þ 20x11þ 30x12þ 40x13þ 30x14þ 45x15þ 40x16 þ 10x17þ 20x18þ 10x19þ 5x20; k3¼ 1 ð½0:3 0 p31 75 70þ ½0:6 0:3 p32 85 75 þ ½1 0:6 p33 115 85Þ; k2 e þ 2þ e2¼ 1; ðfor G3Þ Level 1 Absolute importance
Strong importance Equal
importance Strong importance Absolute importance Level 1
Housing value 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Structure
attributes 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Neighborhood Attributes 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Location attributes Structure attributes 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Neighborhood attributes 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Location attributes Neighborhood attributes 9:1 8:1 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 Location attributes
z3ðxÞ p31 p32 p33 799; 0 p31 75 70; 0 p32 85 75; 0 p33 115 85; z3ðxÞ ¼ 798x1þ 1249x2þ 1148x3þ 1094x4þ 871x5 þ 924x6þ 997x7þ 770x8þ 903x9 þ 990x10þ 950x11þ 850x12þ 800x13þ 1100x14 þ 900x15þ 1000x16þ 840x17þ 850x18þ800x19þ850x20;
x1þ x2þ ... þ x20¼ 1; ðbuy only one houseÞ
0:88x1þ 0:92x2þ 0:94x3þ 0:972x4þ 0:99x5þ 0:97x6 þ 0:95x7þ 926x8þ 0:9x9þ 0:95x10 þ x11þ 0:9x12þ 0:926x13þ 0:94x14þ x15þ 0:972x16 þ 0:9x17þ 0:9x18þ 0:8x19þ 0:8x20 0:8; ðhouse priceÞ x1þ 0:8x2þ x3þ 0:8x4þ 0:8x5þ 0:6x6þ x7þ 0:4x8 þ 0:8x9þ x10þ 0:8x11þ 0:8x12 þ 0:8x13þ 0:8x14þ 0:8x15þ 0:8x16þ 0:8x17þ x18þ 0:8x19
þ 0:8x20 0:8C1; ðthe safety should at least be goodÞ
where xi(i = 1, 2, . . ., 20) are binary variables
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