Proceedings of 2012 International Conference on Fuzzy Theory and Its Applications National Chung Hsing University, Taichung, Taiwan, Nov.16-18, 2012
A Fuzzy TOPSIS Approach for Medical Provider Selection and Evaluation Shuo-Yan Chou Department of Industrial Management,
Anindhita Dewabharata Department of Industrial Management,
National Taiwan University of Science and Technology
National Taiwan University of Science and Technology
Taipei, Taiwan, ROC e-mail:
[email protected] Vincent F. Yu Department of Industrial Management,
Taipei, Taiwan, ROC e-mail:
[email protected] Luu Quoc Dat Department of Industrial Management,
National Taiwan University of Science and Technology
National Taiwan University of Science and Technology
Taipei, Taiwan, ROC e-mail:
[email protected]
Taipei, Taiwan, ROC Email:
[email protected] Since medical tourism is one of the fastest growing tourism markets in the world, numerous studies have investigated the topic [2-14]. Although research studies are abundant, most are usually theoretical or focus on determining the social impacts of medical tourism. There is no study that proposes a methodology for customers to be able to determine the destination of healthcare (medical provider). Many potential criteria, such as a medical provider’s service price and quality, the accommodation’s price and quality, tourism activities, transportation cost, and restaurants’ prices, must be considered in evaluating and selecting a medical provider. Therefore, medical provider selection and evaluation can be viewed as a multiplecriteria decision making (MCDM) problem.
Abstract-The development of health tourism nowadays has significantly increased. Medical tourism resources are not just about medical providers, but also related to accommodations, attractions or tourism activities, transportation, and restaurants that are available at the location of the medical provider. Therefore, customers need a methodology to help them determine the destination of their healthcare (medical providers) based on a set of factors. This paper proposes a fuzzy TOPSIS approach to support the medical provider selection and evaluation process. The proposed model manually collects the ratings of alternatives from various sources on the Internet and expresses the importance weights of the criteria for medical providers in linguistic terms. We then derive the positive and negative ideal solutions based on the normalized weighted ratings. Next, the closeness coefficients are defined to determine the ranking order of alternatives. Finally, we apply the proposed model to a medical provider evaluation and selection problem involving patients from New York in order to demonstrate its applicability and computational process.
In recent years, the technique for order performance by similarity to ideal solution (TOPSIS) has been a popular technique for solving MCDM problems. The fundamental idea of TOPSIS is that the chosen alternative should have the shortest distance from the positive-ideal solution and the farthest distance from the negative-ideal solution, in order to solve MCDM problems. Some recent application can be found in [15-18]. This present paper proposes a fuzzy TOPSIS for medical provider selection and evaluation problem. The proposed model manually collects the ratings of alternatives from various sources on the Internet and expresses the importance weights of criteria for medical providers in terms of triangular fuzzy numbers (TFNs). Then, a closeness coefficient is defined to determine the ranking order of alternatives by calculating the distances of alternatives to both the positive-ideal and negative-ideal solutions. Finally, this paper gives an application for medical provider evaluation and selection to highlight the procedure of the proposed approach.
Keywords: Multiple criteria analysis; Fuzzy TOPSIS; Fuzzy MCDM; Medical provider selection.
I. INTRODUCTION Medical tourism, the act of travelling overseas for treatment and care, has grown rapidly in the past decade. It has been estimated that the total number of medical tourists has increased from 19 million travelers in 2005 to 25.8 million in 2007, which is an annual growth rate of 16.5% [1]. The Deloitte Center for Health Solutions predicted that, in US alone, about 1.6 million Americans will travel abroad for medical care in 2012, with an anticipated yearly growth rate of 35% [2]. In UK, it was estimated that around 60,000 UK patients travelled abroad for medical care in 2010 [3]. Medical tourism enables patients to quickly and conveniently receive medical services through travel, at lower prices and, oftentimes, at better quality than they could in their native countries [4].
The remainder of this paper is organized as follows. Section 2 reviews the basic concepts and definitions of fuzzy numbers. Section 3 proposes a fuzzy TOPSIS approach. The applicability and advantages of the proposed approach is illustrated through an application in section 4. Finally, conclusions are drawn in Section 5.
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Proceedings of 2012 International Conference on Fuzzy Theory and Its Applications National Chung Hsing University, Taichung, Taiwan, Nov.16-18, 2012 TABLE 1. TFNs OF LINGUISTIC VARIABLES FOR RATING OF ALTERNATIVES AND IMPORTANCE WEIGHTS OF CRITERIA
II. FUZZY SETS THEORY This section reviews some basic notions and definitions of fuzzy sets and fuzzy numbers as follows [19-20].
Ratings Linguistic variables
2.1. Fuzzy sets A (x, f A (x)) | x U
where U is the universe of discourse, A is a fuzzy set in U , f ( x) is defined as a membership function f A ( x) [0,1], A
for f A ( x), x U , indicates the degree of x in A. 2.2. Triangular fuzzy number
(e) (f)
1 = Terrible (T)
(0.0, 0.1, 0.2)
2 = Poor (P)
(0.1, 0.3, 0.5)
3 = Average (A)
(0.3, 0.5, 0.7)
4 = Good (G)
(0.6, 0.8, 0.9)
5 = Excellent (E)
(0.8, 0.9, 1.0)
Unimportant (UI) Less Important (LI) Important (IM) More Important (MI) Very Important (VI)
TFNs
(0.0, 0.1, 0.3) (0.2, 0.3, 0.4) (0.3, 0.5, 0.7) (0.7, 0.8, 0.9) (0.8, 0.9, 1.0)
This study develops a fuzzy TOPSIS approach for selecting and evaluating a medical provider, by the following six-step procedure. Step 1. Aggregate ratings of alternatives versus the criteria Assume that sets of users U t , t 1, 2,..., k are responsible for evaluating m alternatives ( Ai , i 1, 2,..., m) under h selection criteria (C j , j 1, 2,..., h ). Let xijt (eijt , fijt , gijt ) , i 1,..., m, j 1,..., h, t 1,..., k , be
f A is strictly increasing on [ a , b ]; f A (x) 1, for x b f A is strictly decreasing on [ b , c ]; f A ( x) 0, for all x c, ,
the suitability rating assigned to alternative Ai , by sets of users Ut , for criterion C j . The averaged suitability rating, xij (eij , fij , gij ), can be evaluated as [21]:
where a, b, c are real numbers. Unless elsewhere specified, this research assumes that A is convex and bounded (i.e. a, c ). A fuzzy number A can be denoted as a triplet A (a, b, c), and the membership function f ( x ) is expressed as:
xij
A
1 ( xij1 xij 2 ... xijt ... xijk ), k
(3)
k k k where eij 1 eijt , fij 1 fijt , and gij 1 gijt . k t 1 k t 1 k t 1
a x b, ( x a ) / (b a), f A ( x ) ( x c) / (b c), b x c, (1) 0, otherwise. Let A1 (a1 , b1 , c1 ), and A2 (a2 , b2 , c2 ) be two triangular fuzzy numbers. A distance measure function d ( A1 , A2 ) can be defined as [15]
d ( A1 , A2 )
Linguistic variables
III. MODEL ESTABLISHMENT
A TFN A is described as any fuzzy subset of the real line R with membership function f A ( x ) that can be generally be defined as: (a) f A is a continuous mapping from R to the closed interval [0,1]. (b) f A ( x) = 0, for all x , a ; (c) (d)
Importance weights TFNs
Step 2. Aggregate the importance weights Let w jt (o jt , p jt , q jt ),w jt R* , j 1, , h, t 1, , k
be
the weight assigned by a set of users U t to criterion C j . The average weight, w j (o j , p j , q j ) , of criterion C j assessed by k sets of users can be evaluated as:
1 [(a1 a2 ) 2 (b1 b2 ) 2 (c1 c2 ) 2 ] (2) 3
w j (1/ k ) ( w j1 w j 2 ... w jk )
2.2. Linguistic variable and fuzzy numbers A linguistic variable is a very useful concept in dealing with situations that are too complex or not well-defined enough to be reasonably described in traditional quantitative expressions. Table 1 lists the linguistic variables for rating the alternatives and importance weights of the criteria.
(4)
where o j (1/ k ) k o jt , p j (1/ k ) k p jt , q j (1/ k ) k q jt . t 1 t 1 t 1 Step 3. Normalize the performance of alternatives versus the objective criteria This paper classifies the criteria into benefit (B) and cost (C). A benefit criterion has the characteristic of “the larger the better”. A cost criterion has the characteristic of “the smaller the better”. To ensure compatibility between average ratings and average weights, the average ratings are normalized into comparable scales. Suppose is the performance of alternative ion rij (aij , bij , cij ) criteria j. The normalized value xij can then be denoted as [15]:
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Proceedings of 2012 International Conference on Fuzzy Theory and Its Applications National Chung Hsing University, Taichung, Taiwan, Nov.16-18, 2012
aij bij cij xij * , * , * , j B cj c j cj aj aj aj xij , , , j C cij bij aij
and restaurants, and transportation cost from various sources on the Internet. In particular, data on health care providers including their location are obtained from the website All Medical Tourism (http://www.allmedicaltourism.com/doctor/). Data on accommodations, attractions, restaurants, and their users’ ratings are taken from the website Trip Advisor (http://www.tripadvisor.com/). Data were obtained by conducting a query based on information of themedical providers’ location, such as country and city. The transportation cost data were obtained from the website Expedia (http://www.expedia.com) by performing a query based on place of origin of the traveler, destination, and desired time period, and from the results obtained, what the average cost is of airlines serving the route.
(5)
where a j min i aij , c*j max i cij , i 1, , m; j 1, , n. Step 4. Calculate normalized weighted rating The normalized weighted ratings Gi are calculated by multiplying the normalized average rating xij with its associated weights w jt as
Gi xij wj , i 1,, m, j 1,, h.
(6)
After preliminary screening, we choose three medical providers, including Asklepion ( A ), FV Hospital ( A2 ), and
Step 5. Calculate of A , A , di and d i
1
CostaMed ( A3 ), for further evaluation and selection. During the users’ relevance feedback collection, three sets of users U1 ,U 2 , and U 3 , which include 205 users, are collected to evaluate the three medical providers based on five aspects: medical providers’ service price and quality (C ), hotels’ quality and price (C ), tourism activities (C ), restaurants’ quality and price (C ), and air fare (C ), on a scale of 1 to 5 (1 = Terrible; 2 = Poor; 3 = Average; 4 = Good; 5 = Excellent).
The fuzzy positive-ideal solution (FPIS, A ) and fuzzy negative-ideal solution (FNIS, A ) are obtained as: A max{Gi }
(7)
A min{Gi }
(8)
i
i
1
The distances of each alternative Ai , i 1, , m from A and A are calculated as:
n
di
(G A )
2
i
Step 1. Aggregate the ratings of alternatives versus the criteria Table 2 presents the average users’ ratings of medical providers A1 , A2 and A3 under each criterion C1 , C2 , C3 , C4
n
(G A )
2
i
(10)
j 1
where d i represents the shortest distance of alternative Ai , and d i represents the farthest distance of alternative Ai .
and C5 . By “(3)”, we can obtain the suitability and aggregated ratings of alternatives by linguistic terms, as shown in Table 2. From “(5)”, the data of transportation costs and the transformed values for each medical provider are shown in Table 3.
Step 6. Calculate the closeness coefficient The closeness coefficient of each alternative, which is usually defined to determine the ranking order of all alternatives, is calculated as:
CCi
di di di
3
5
The computational procedure is summarized as follows.
(9)
j 1
d i
2
4
(11)
A higher value of the closeness coefficient indicates that an alternative is closer to PIS and farther from NIS simultaneously. The closeness coefficient of each alternative is used to determine the ranking order of all alternatives and identify the best one among a set of given feasible alternatives. IV. APPLICATION This section uses a medical provider evaluation and selection problem to demonstrate the feasibility and advantages of the proposed approach. This paper manually collects the information of medical providers, patients’ ratings of accommodations, attractions
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Proceedings of 2012 International Conference on Fuzzy Theory and Its Applications National Chung Hsing University, Taichung, Taiwan, Nov.16-18, 2012
Crit eria
Average values of each set
Medica l provide rs A1
C1
C2
C3
C4
set U1
set U2
set U3
4.5
5
4
(0.7, 0.85, 0.95)
4
4
(0.6, 0.8, 0.9)
A3
5
5
4.5
(0.75, 0.88, 0.975)
A1
5
4
4.5
(0.7, 0.85, 0.95)
A2
4.5
4
4.5
(0.68, 0.84, 0.94)
A3
4
5
4.5
(0.7, 0.85, 0.95)
A1
4
4
4.5
(0.65, 0.825, 0.925)
A2
3.5
4
4.5
(0.583, 0.767, 0.883)
A3
2.5
4
3.5
(0.38, 0.58, 0.74)
A1
4
4.5
4.5
(0.68, 0.84, 0.94)
A2
4.5
4.5
4.5
(0.7, 0.85, 0.95)
A3
4.5
4
4.5
(0.68, 0.84, 0.94)
TABLE 4. IMPORTANCE WEIGHTS OF THE CRITERIA AND THE AGGREGATED WEIGHTS
C1 C2 C3 C4 C5
D2
D3
VI MI I MI MI
VI MI MI MI MI
VI MI MI MI VI
d
A1
1.741
2.330
A2
1.773
2.307
A3
1.671
2.432
Medical providers
Closeness coefficient
Ranking
A1
0.572
2
A2
0.565
3
A3
0.593
1
V. CONCLUSIONS In this paper we have proposed a fuzzy TOPSIS approach to support the medical provider selection and evaluation process. Using the proposed approach, the patients can determine suitable medical providers based on five aspects, including medical providers’ service price and quality, hotels’ quality and price, tourism activities, restaurants’ price and quality, and airfare. The proposed model manually collected the ratings of alternatives from various sources on the Internet and expressed the importance weights of criteria for medical providers in terms of triangular fuzzy numbers. We then defined the closeness coefficients to determine the ranking order of alternatives. The application in this study showed that the computational procedure is efficient and easy to implement. Thus, for practitioners, the proposed approach is a very effective tool to solve MCDM problems. Future research may apply the proposed approach to other MCDM problems with similar settings in various industries.
Step 2. Aggregate the importance weights Table 1 shows the linguistic weighting set and related fuzzy numbers employed to assess the importance of all the criteria. The importance and aggregated weights of the five criteria from the three sets of users are obtained by “(4)” and expressed in Table 4.
Users
d
TABLE 6. CLOSENESS COEFFICIENTS OF THREE MEDICAL PROVIDERS
Transformed Airfare (NY) C5 0.748 0.822 1
D1
Medical providers
Step 5. Obtain the closeness coefficient Table 6 shows the closeness coefficients of alternatives by using “(11)”. Therefore, the ranking order of three medical providers is A3 A1 A2 . So, for patients from New York, the best medical provider is A3 .
TABLE 3. DATA OF AIRFARES AND THE TRANSORMED VALUES OF EACH MEDICAL PROVIDER
Criteria
TABLE 5. DISTANCE MEASUREMENT OF EACH MEDICAL PROVIDER
4
Air-fare (NY) C5 1,098 999 821
rij
A2
Medical providers A1 A2 A3
Step 4. Calculate A , A , di and d i Table 5 shows the distance of each medical provider from A and A by using “(7)”-”(10)”.
TABLE 2. RATINGS OF ALTERNATIVES VERSUS QUALITATIVE CRITERIA
rij (0.8, 0.9, 1.0) (0.7, 0.8, 0.9) (0.567, 0.7, 0.833) (0.7, 0.8, 0.9) (0.733, 0.833, 0.933)
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Step 3. Calculate normalized weighted rating Using “(6)”, the normalized weighted ratings are obtained.
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