Fuzzy Simple Additive Weighting for Evaluating a Personalised Geographical Information System Katerina Kabassi Abstract This paper presents how a fuzzy multi-criteria decision making theory has been used for evaluating personalised software. More specifically, the fuzzy simple additive weighting theory has been used for the evaluation of a Geographical In-formation System. The Geographical Information System has the ability to process information about its users in order to adapt its interaction to each user dynamically. The proposed system has been evaluated in comparison to a standard GIS using linguistic terms. These terms were further translated to fuzzy numbers in order to calculate a crisp value for each GIS aggregating all the criteria taking into account. The comparison of the crisp value for the two GISs revealed that the personalised GIS is friendlier and more useful than the standard one.
1 Introduction Geographical Information Systems have been used lately extensively in many different domains, e.g. economical and regional development, environmental management, tourism sector etc. However, a main problem of such systems is that not many users have the specialised knowledge that is required to use them. Furthermore, the increasing complexity of the world and information overload makes it nearly impos-sible for a Geographical Information System (GIS) to be able to address the needs of large and diverse user populations. As a result, lately, a lot of research energy has been put on developing systems that are user friendly and can provide personalised interaction. Therefore, several AI methods and approaches such as Bayesian Networks, multicriteria decision making and fuzzy logic have been used for personalising interaction in a GIS [1, 2, 3, 4]. In view of the above, a Geographical Information System called ADAPTIGIS (Adaptive GIS) was developed [5]. The particular system contains data Department of Ecology and the Environment, Technological Educational Institution of Ionian Islands, 2 Kalvou Sq., 29100 Zakynthos, Greece e-mail:
[email protected]
E. Damiani et al. (Eds.): New Direct. in Intel. Interactive Multimedia Sys., SCI 226, pp. 275–284. springerlink.com c Springer-Verlag Berlin Heidelberg 2009
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about the physical and anthropogenic environment of Zakynthos, an island of Greece. More specifically, ADAPTIGIS has the ability to process information about the users so that the system can adapt its interaction to each user dynamically. The information is processed using a multi-criteria decision making theory [6].
However, the incorporation of some kind of theory does not guarantee the successful reasoning of the system. Mc Tear [7] points out that the relationship between theory and practice is particularly important in Intelligent Interface Technology as the ultimate proof of concept here is that the interface actually works and that it is acceptable to users; for this reason practical issues such as performance, reliability and usability would seem to be more important than theoretical issues such as choice of system design methodology or specification notations. Indeed, Chin [8] points out that empirical evaluations are needed to determine which users are helped or hindered by user-adapted interaction in user modelling systems. He adds that the key to good empirical evaluation is the proper design and execution of the experiments so that the particular factors to be tested can be easily separated from other confounding factors. However, he notes that empirical evaluations are not so common in the user modelling literature. Many researchers have also stated that it is important when evaluating adaptive systems to assess whether the system works better with the user modelling component as opposed to a system deprived of this component [8, 9, 10]. In view of the above, ADAPTIGIS was evaluated in comparison to a standard GIS that does not incorporate any intelligence using Fuzzy Simple Additive Weighting (FSAW) [11]. Indeed, the evaluation of software involves several criteria and, there-fore, can be considered as a multi-criteria problem. Especially, the FSAW theory was selected because it is rather simple and has the advantage of allowing multi-criteria problems to accommodate linguistic terms represented as fuzzy numbers. This facilitates the creation of a decision procedure that is more realistic than other existing theories [11].
2 Fuzzy Simple Additive Weighting Zadeh [12] pioneered the use of Fuzzy Set Theory (FST) to address problems involving fuzzy phenomena. In a _universe of discourse X , a fuzzy subset A of X is _
defined with a membership function μ (x) that maps each element x in X to a real _ (x) signifies the grade of number in the interval [0, 1]. The function value of μ α _ _ α
bership of x in A. When
mem-
_
_
α
μ (x) is large, its grade of membership of x in A is strong
[13]. A fuzzy set A = (a, b, c, d) on R, a < b < c < d, is called a trapezoidal fuzzy number if its membership function is
Fuzzy Simple Additive Weighting . . .
277
(x a) −
, a
μ (x) = 1,
≤x≤b
≤ ≤
(b−a)
_
b x c , c x d 0, otherwise where a, b, c, d are real numbers [13, 14]. Trapezoidal fuzzy numbers are the most widely used forms of fuzzy numbers because they can be handled arithmetically and interpreted intuitively. The FSAWS procedure based on above conceptual model is as follows: Step 1: Form a committee of decision-makers. Choose the attributes and identify the prospective alternatives. A committee of decision-makers is formed to determine the most appropriate alternative. Step 2: Determine the degree of importance (or reliability) of the decision-makers. If the degrees of importance (or reliability) of decision-makers are equal, then the = Ik group of decision-makers is deemed a homogeneous group I1 = I2 = 1 = k ; otherwise, the group of decision-makers is called a heterogeneous (nonhomogeneous) group. Step 3: Introduce linguistic weighting variables (Table 1) for decision-makers to assess attributes importance, and compute aggregated fuzzy weights of individα
≤ ≤
d)
(x
−
(c−d)
···
_
=( ,
,
),
,
= , ,...,
= , ,...,
ual attributes. Let Wjt a jt b jt c jt d jt j 1 2 n; t 1 2 k be the lin-guistic weight given to subjective attributes C1,C2, . . . ,Ch and objective attributes
C _h+1
,C h+1
, . . . ,C by decision-maker D . The aggregated fuzzy attribute weight, n
t
Wj = (a j , b j , c j , d j ), j = 1, 2, . . . , n of attribute C j assessed by the committee of k decision makers is defined as Wj = (I1 ⊗Wj1) (I2 ⊗Wj2) I1k ⊗Wjk), where k k k k a j = ∑t =1 It a jt , b j = ∑t =1 It b jt , c j = ∑t =1 It c jt , d j = ∑t =1 It d jt . Step 4: Defuzzify the fuzzy weights of individual attributes; compute the normalized weights and construct the weight vector. To defuzzify the weights of the fuzzy attributes, the signed distance is adopted. The _
_
_
⊕
_
⊕···⊕
_
_
defuzzification of Wj , denoted as d(Wj ) is therefore given by _
1
d(Wj ) = 4 (a j + b j + c j + d j ), j = 1, 2, . . . , n The crisp value of the normalized weight for attribute C j denoted as Wj , is given by: _
Wj =
d(Wj )
∑nj=1 d(Wj ) _
, j = 1, 2, . . . , n
where ∑ j=1 Wj = 1.The weight vector W = [W1,W2, . . . ,Wn ] is therefore formed. Step 5: Use linguistic rating variables (Table 2) for decision-makers to assess fuzzy ratings of alternatives with respect to individual subjective attributes, and then pool _ them to obtain the aggregated fuzzy ratings. Let x i jt = (oi jt , pi jt , qi jt , si jt ), i = 1, 2, . . . , m, j = 1, 2, . . . , h, t = 1, 2, . . . , k be the linguistic suitability rating assigned to alternative location Ai for subjective attribute C j by decision-maker Dt . Let us _ further define x i jt as the aggregated fuzzy rating of alternative Ai for n
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subjective attribute C j , such that _
⊕
_
⊕···⊕ I1k ⊗ x i jk)
_
_
x i j = (I1 ⊗ x i j1) (I2 ⊗ x i j2) which can subsequently be represented and computed as _
x i j = (oi j , pi j , qi j , si j ), i = 1, 2, . . . , m, j = 1, 2, . . . , h k k k k where oi j = ∑t =1 It oi jt , pi j = ∑t =1 It pi jt , qi j = ∑t =1 It qi jt , si j = ∑t =1 It si jt . Step 6: Construct a fuzzy rating matrix based on fuzzy ratings. The fuzzy rating matrix M can be concisely expressed in matrix format _
_
_
x 1
x 11 _
x 12
x
_
21
_
M=
··· 22
· · ·· ·· _
_ xm1 xm2
∀
_
x _
n x _
···
2n
· ··· · · _
··· x
mn
where x i j , i, j is the aggregated fuzzy rating of alternative Ai, i = 1, 2, . . . , m with respect to attribute C j .
Step 8: Derive total fuzzy scores for individual alternatives by multiplying the fuzzy rating matrix by their respective weight vectors. Obtained total fuzzy score vector by multiplying the fuzzy rating matrix M by the corresponding weight vector W , i.e.,
F=M
⊗
W
T
=
x11
x12
x21
x22 ·
··· x ··· x
· · · · ·
···
x
x
m1
1n
W1 x11 ⊗W1
·
2n
· ·
W2 ⊗
·
x
m2 ···
· ·
mn
Wn
_
⊕ x12 ⊗W2 ⊕ . . . x1n ⊗Wn x W 12 ⊗ 1 ⊕ x22 ⊗W2 ⊕ . . . x2n ⊗Wn = ·· = · x x m1 ⊗W1 ⊕ m2 ⊗ W2 ⊕ . . . xmn ⊗ Wn
f2 ·
· ·
=
m∗1
f i
fn
where fi = (ri , si , ti, ui), i = 1, 2, . . . , m. Step 9: Compute a crisp value for each total score using a defuzzification method and select the alternative(s) with the maximum total score. Rank total fuzzy scores f1 , f2 , . . . , fm by the signed distance to determine the best location. Determine crisp total scores of individual locations by the following defuzzification equation: _
_ _
_
_
1
d( fi ) = 4 (ri + si + ti + ui), i = 1, 2, . . . , m
( )
where d fi gives the defuzzified value (crisp value) of the total fuzzy score of location Ai by using the signed distance. The ranking of the locations can then be preceded with the above crisp value of the total scores for individual alternatives.
Fuzzy Simple Additive Weighting . . .
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3 Geographical Information System ADAPTIGIS is a Geographical Information System that contains data about the physical and anthropogenic environment of Zakynthos, an island of Greece [5, 6]. The particular island has great touristic as well as ecological interest due to Lagana Bay, where the turtles Caretta-Caretta live and breed. For this purpose, the informa-tion that is maintained in such a GIS would be of interest to a great variety of users. However, different kinds of users may have different interests, needs and back-ground knowledge. For example, tourists and/or residents of the islands would prefer to find information about roads, summer resorts and cultural information, e.g. monuments and churches. Environmentalists, ecologists and researchers, on the other hand, may seek low/high resolution satellite data, which are used for the es-timation, charting, characterization and classification of various environmental pa-rameters such as land cover/usage, geomorphological features, etc. In view of the above, the main characteristic of ADAPTIGIS is that it can adapt its interaction with each individual user. In order to adapt the information provided to the interests and background knowledge of each user interacting with ADAPTIGIS, the system incorporates a user modelling component. This component maintains information about the interests, needs and background knowledge of all categories of potential users. The information that is collected for every category of users has been based on the analysis of the results of the empirical study [6]. More specifically, the potential users of the GIS were divided into five stereotypes in accordance to the five main categories of users that were identified: Residents of the islands, Tourists, Local authorities of Zakynthos, Environmentalists / Researchers, Students of the department of ecology and the environment in the Technological Educational Institution of the Ionian islands, which is located in Zakynthos. Users were also categorised into one of three stereotypes taking into account his/her believed level of expertise in computers and the Internet: novice, intermediate and expert and correspond to low, medium and high of expertise in ICT, respectively. For example, if a user has no computer skills then s/he is categorised as novice. The body of the stereotype consists of some default assumptions about the users belonging to that specific stereotype. More specifically, in the proposed approach in ADAPTIGIS, default assumptions are parameterized and are given in the form of values for the criteria defined during analysis. In this way, stereotypes can easily be combined with the decision making model for providing personalized interaction.
The main feature of ADAPTIGIS is that it can adapt its interaction with each user. In order to evaluate different information, the system uses a simple decision making model. The suitability of each map for the particular user interacting with the sys-tem is estimated taking into account some criteria. • Degree of Interest (i): The values of this criterion show how interesting each information about Zakynthos is for the particular user. • Need for information (n): This criterion shows how important each information about Zakynthos is for the particular user.
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• Comprehensibility of the information(c): This criterion also shows how compre-hensible each information about Zakynthos is to the particular user. • Level of computer skills (l): This criterion shows how comprehensible the way of presentation of each information about Zakynthos is to the particular user. The values of these criteria are estimated taking into account the information that is stored in the user modeling component of the system. This component stores information about each individual user interacting with the GIS. For the evaluation of the geographical information, the reasoning mechanism of the system uses the SAW method [15, 16]. According to the SAW method the multi-criteria function is calculated as a linear combination of the values of the four criteria that had identified in the previous experiments: U (X j ) = ∑ wici j , where wi are the weights of criteria and ci j are the values of 4
i=1
the criteria for the X j geographical information (map). The criteria used for the evaluation of the geographical information are considered equally important and, therefore, the formula for the calculation of the multi-criteria function is formed: U (X j ) = 0.37i + 0.30n + 0.20c + 0.13l
(1)
In view of the values of the multi-criteria function for the different geographical information, the maps are ranked and the one with the highest value is considered to be the most suitable for the user that interacts with the system.
4 Evaluation Experiment For the evaluation of the Adaptive GIS, the evaluation experiment was designed taking into account the steps of the FSAW method. For this purpose a committee of the decision-makers was formed to evaluate ADAPTIGIS. The committee of decision makers was consisted of 12 users that were randomly selected; 2 environmentalists, 4 students, 4 tourists and 2 software engineers. The group of decision makers was homogeneous as the reliability (importance) of the decision-makers was equal. The criteria that were taken into account for the evaluation of the Adaptive GIS was:
• Interest satisfaction (Is): this criterion reveals how successful the system was in addressing the users’ interests. • Information completeness (Ic): this criterion shows how successful the system was in providing all the appropriate information to the user interacting to the system. • Needs fulfillment (Nf): this criterion shows how successful the system was in addressing the users’ needs and presenting the appropriate information to the user.
Fuzzy Simple Additive Weighting . . .
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• User friendly (Uf): the specific criterion shows what the users think about the interaction with the adaptive system, whether it is intrusive or not, whether it provides natural interaction etc. The decision makers were first asked to evaluate the above mentioned attributes with respect to their importance in adaptive software evaluation. This procedure resulted in aggregated fuzzy weights of individual attributes. For the evaluation of the above mentioned criteria the decision makers used the linguistic variables presented in table 1. Linguistic variables Fuzzy numbers Very low (VL) (0, 0, 0, 3) Low (L) (0, 3, 3, 5) Medium (M) (2, 5, 5, 8) High (H) (5, 7, 7, 10) Very high (VH) (7, 10, 10, 10)
Table 1: Linguistic variables and fuzzy numbers for the importance weight.
As soon as all the linguistic variables of the criteria weights were collected, the fuzzy weights of the criteria are calculated. More specifically, each linguistic vari-able is translated to a fuzzy number as this is presented in table 1. These values are used for calculating the aggregated fuzzy weight for each one of the four attributes: W Is = (15.5, 23, 23, 29), WIc = (9.25, 17, 17, 25.75), WN f = (23, 20.5, 20.5, 28), W _ U f = (11.5, 19.5, 19.5, 27). These weights are defuzzified according to the step 4 _
_
_
_
_
_
_
of the theory: d(WIs ) = 22.63, d(WIc ) = 17.25, d(WN f ) = 20.50, d(WU f ) = 19.38. The crisp values of the normalized weights are calculated:
W Is
_ d(WIs )
=
4
∑ j= 1
W
_
W Nf
_
Is
d(WN f )
=
∑
4
W
=
_
22.63
= 0.28 , WIc
=
20.50
W
4
=
_
∑ j =1 Ic _ dW
79.76 =
_ d(WIc )
= 0.26 , WU f =
(
= 0.22 ,
79.76
U f)
W
_
4
17.25
=
19.38
= 0.24 ,
∑ j=1 U f 79.76 79.76 The weight vector is, therefore, formed to W = (0.28, 022, 026, 024). j=1
Nf
5 Results The 12 users were asked then to evaluate ADAPTIGIS using the linguistic rating variables presented in Table 2 with respect to the four attributes.
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Katerina Kabassi Linguistic variables Very poor (VP) Between very poor and poor (B. VP & P) Poor (P) Between poor and fair (B. P & F) Fair (F) Between fair and good (B. F & G) Good (G) Between good and very good (B. G & VG) Very good (VG)
Fuzzy numbers (0, 0, 0, 20) (0, 0, 20, 40) (0, 20, 20, 40) (0, 20, 50, 70) (30, 50, 50, 70) (30, 50, 80, 100) (60, 80, 80, 100) (60, 80, 100, 100) (80, 100, 100, 100)
Table 2: Linguistic variables and fuzzy numbers for the ratings.
The linguistic rating variables were processed using the formulae of step 5 of the algorithm in order to obtain the aggregated fuzzy ratings. The detailed presentation of the calculations is beyond the scope of this paper and, therefore, only the results of this processing are presented in the fuzzy rating matrix (Table 3).
Is Ic Nf Uf ADAPTIGIS (185,245,255,285) (117.5,177.5,200,255) (97.5,157.5,195,255) (127.5,187.5,220,270) Standard GIS (45,85,85,145) (67.5,117.5,137.5,197.5) (22.5,72.5,87.5,147.5) (142.5,202.5,235,285)
Table 3: Fuzzy rating matrix. ADAPTIGIS seems to be winning the standard GIS in most attributes. However, the standard GIS was considered by 2 users as user friendlier and non intrusive. In order to derive the total fuzzy scores for individual alternative, the fuzzy rating matrix is multiplied by the corresponding weight vector W . 185, 245, 255, 285 117.5, 177.5, 200, 255 97.5, 157.5, 195, 255 127.5, 187.5, 220, 270 F = 45, 85, 85, 145 67.5, 117.5, 137.5, 197.5 22.5, 72.5, 87.5, 147.5 142.5, 202.5, 235, 285
= (134.2, 194.2, 219.4, 267.3)
0.28 0.22 ⊗ 0.26 0.24
=
F
(67.5, 117.1, 133.2, 190.8)
The crisp value for each total score is computed using the defuzzification method. _
1
d( f1) = 4 (134.2 + 194.2 + 219.4 + 267.3) = 203.8 _
1
d( f2) = 4 (67.5, 117.1, 133.2, 190.8) = 127.2 The crisp value of the first alternative that corresponds to ADAPTIGIS is much higher than the crisp value of the standard GIS. Therefore, the users seem to prefer in general ADAPTIGIS than a standard GIS.
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6 Conclusions In this paper, we described how a fuzzy multi-criteria decision making theory can be used for evaluating a per-sonalised GIS. The theory that was selected was the FSAW theory. The particular theory is very simple and uses linguistic terms. Indeed, previous studies (e.g. [19]) revealed that users had a difficulty in quantifying criteria while evaluating a software system. Therefore, in this case, FSAW was selected that uses linguistic terms that can be further translated into fuzzy numbers. This results in making the procedure more realistic, suitable, user friendly and effective.
The evaluation experiment revealed that the users could express themselves better using linguistic terms and, therefore, preferred this evaluation setting than others that use number rating. Furthermore, the evaluation results proved that the personalised GIS described in this paper surpass a standard GIS in selecting the information that is most useful for a particular user.
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