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# QoS-Aware Web Services Selection Based on Fuzzy Dominance

Amal Halfaoui, Fethallah Hadjila, Fedoua Didi

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Amal Halfaoui, Fethallah Hadjila, Fedoua Didi. QoS-Aware Web Services Selection Based on Fuzzy Dominance. 5th International Conference on Computer Science and Its Applications (CIIA), May 2015, Saida, Algeria. pp.291-300, 10.1007/978-3-319-19578-0_24. hal-01789939

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Submitted on 11 May 2018

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# QoS-aware Web services Selection based on Fuzzy Dominance

Amal Halfaoui, Fethallah Hadjila, and Fedoua Didi

Computer Science Departement,
Tlemcen University, Algeria

{a_halfaoui,f_hadjila,f_didi}@mail.univ-tlemcen.dz

http://www.univ-tlemcen.dz/

**Abstract.** The selection of an appropriate web service for a particular task has become a difficult challenge due to the increasing number of web services offering similar functionalities. Quality of web services (QoS) becomes crucial for selecting web services among functionally similar components. However, it remains difficult to select an interesting Web services from a large number of candidates with a good compromise between multiples QoS aspect. In this paper, we propose a novel concept based on dominance degree to rank functionally similar services. We rank Web services by using a fuzzification of Pareto dominance called Average-Fuzzy-Dominated-Score(*AFDetS*()). We demonstrate the effectiveness of the *AFDetS* through a set of simulations by using a real Dataset.

**Keywords:** web service selection, dominance, Skyline, Ranking, QoS

## 1 Introduction

Nowadays, an increasing number of Web services is published and accessible over the web, they are designed to perform a specific task, which essentially consists of either altering the word state (e.g., an on line shopping service) or returning some information to the user (e.g., news Web service).

As the Web is populated with a considerable number of Web services, there exists a large number of service providers competing to offer the same functionality, but with different Quality Of Service (QoS) such as response time, price, etc. Consequently, QoS is thus a crucial criterion to select among functionally similar Web services.

**Example.** Consider a Web service for sending SMS, there are many Web services providing this functionality (e.g., Click Send, Inteltech, Etc.), but with different QoS. Table1 provides such functionality along with real QoS parameters taken from the publicly available Quality of Web services data.<fnref n="1" /> Web services were obtained by using the keyword SMS which represents the tag associated to the functionality of the desired Web services. Each Web service has four QoS parameters *q*₁, *q*₂, *q*₃ and *q*₄, says respectively Response Time, Throughput

<footnote n="1">¹ http://www.uoguelph.ca/qmahmoud/qws</footnote>
(i.e.,Total Number of invocations/period of time) Reliability (Ratio: number of error messages/total messages) and Best Practices (the respect of the specifications). To select an adequate Web service, users need to examine all of them

<table><caption>**Table 1.** A set of Sending SMS Web Services</caption><thead><tr><th>Service provider</th><th>operation</th><th>q1(ms)</th><th>q2(hits/sec)</th><th>q3(%)</th><th>q4(%)</th></tr></thead><tbody><tr><td>S<sub>1</sub> acrosscommunications.com</td><td>SMS</td><td>113.8</td><td>5.2</td><td>81</td><td>84</td></tr><tr><td>S<sub>2</sub> sjmillerconsultants.com</td><td>SMS</td><td>179.2</td><td>0.7</td><td>65</td><td>69</td></tr><tr><td>S<sub>3</sub> webservicex.net</td><td>SendSMS</td><td>1308</td><td>6.3</td><td>67</td><td>84</td></tr><tr><td>S<sub>4</sub> webservicex.net</td><td>SendSMSWorld</td><td>3103</td><td>5.3</td><td>79.3</td><td>91</td></tr><tr><td>S<sub>5</sub> smsinter.sina.com.cn</td><td>SMSWS</td><td>751</td><td>6.8</td><td>64.3</td><td>87</td></tr><tr><td>S<sub>6</sub> sms.mio.it</td><td>SendMessages</td><td>291.07</td><td>5.2</td><td>53.6</td><td>84</td></tr><tr><td>S<sub>7</sub> www.barnaland.is</td><td>SMS</td><td>436.5</td><td>4.5</td><td>43.2</td><td>84</td></tr><tr><td>S<sub>8</sub> emsoap.net</td><td>emSoapService</td><td>424.54</td><td>4.3</td><td>11.9</td><td>80</td></tr></tbody></table>

manually. The user may also face difficulties in balancing between different quality metrics. The skyline presents a good solution for reducing the number of candidate Web services [1],[2] and simplifying the process of selection as it overcomes the major limitation of the current approaches that require users to assign weights over different QoS attributes. The skyline is a subset of Web services that are not (Pareto) dominated by any other Web service. A Web service $S_i$ is said to Pareto dominate another Web service $S_k$ if and only if $S_i$ is better than or equal to $S_k$ in all QoS parameters and better than $S_k$ in at least on one QoS parameter.

According to our example (Table1), the service $S_1$ dominates $S_6, S_7, S_8$. Services $S_1, S_3, S_4, S_5$ belong to the skyline and they are no comparable between them. We can remark that computing skyline reduce the candidate services, in our example we eliminates 50% of the candidate services. However, it remains a challenge to compute skylines in high dimensional data [3],[4]. In addition to that, on the report of [5] the authors show that the skyline may lose some interesting Web services like $S_6$ which is dominated by $S_4$ while $S_4$ is the worst service in term of response time, however $S_6$ has a good response time and is closer to $S_4$ on the other QoS parameters.

Motivated by this, we propose an extension of Pareto dominance relationship called Averaged-Fuzzy-Dominated-score *AFDetS*() to associate a score to each service and rank them. We also propose a comparison between the dominated-score *AFDetS* and Dominating score used in [5] and confirm that the use of the Dominated score is more interesting than the Dominating score in Ranking service, this fact is also confirmed in [19]. The rest of the paper is organized as follows. In the next section, we discuss related work. In Section 3, we provide the formal definition of *AFDetS* and show it application on our example Table1. Section 4 presents the results of our experimentation. Finally, section 5 gives conclusions and an outlook on possible continuations of our work.
## 2 Related work

A lot of efforts have been devoted to the problem of QoS-aware Web service selection. Some of them use the linear programming technique [7], [8]. Linear programming techniques are used in [7] to find the optimal selection of component services and gives an extensible model to evaluate the QoS parameters. Linear programming techniques are extended in [8] to include local constraints. Others work use combinatorial model and graph model [9] where the authors use heuristic algorithm to solve the problem of service selection with multiple QoS constraints. In [10] the authors present a selection algorithm to evaluates multiples QoS based on an ontology. Nevertheless, the majority of these approaches are more suitable for limited number of Services(the selection process has an exponential space complexity) and limited number of QoS, especially when the users has to assign weights on QoS attributes.

In recent research, the skyline paradigm is introduced as a good and efficient mechanism to reduce the number of service candidates and simplify the process of selection. The idea of skyline comes from the old research like contour problem, maximum vector and convex hull and was introduced into databases by Borzsonyi [11] who develops three algorithms: BNL, DC and B-tree, this leads to develop and ameliorate several other algorithms like SFS [12], SaLSa [13], Zorder, [14] and NN[3]. Some of these algorithms exploit index structures like [14],[3] to enhance the skyline computation process. However, the size of skyline increases under a high number of QoS and sometimes privileges Web services with bad compromise between QoS.

To handle the problem of large skyline, some works combine the advantage of the skyline and ranking and define variants of skyline like [1],[15],[16] and [17]. In [15] the authors present skyline frequency concept which is the number of subspaces where a point p is skyline, however this lead to calculate skyline of all subspaces and results in a high computational time, further more authors introduce an approximate algorithm to reduce the computation space. In [1] Chan et al. present the notion of k-dominance which relax the pareto dominance to a subset of k parameters, however there exists cyclic dominance relationship (CDR) which leads to the loss of skylines in addition k-dominance often returns an empty set. In [17] Lin et al. propose top-krepresentative skyline but this method is more suitable for anti-correlated data [18] in addition to that, k-representative skyline is considered as NP-hard for more than three dimensional dataset. In [16] the authors present the skyline graph which maps the dominance of different skyline subspaces into a weighted directed graph and use link-based techniques to rank skyline, however, the problem of dominance on a large space is still solved. These approaches rely on Pareto dominance relationship thus, they don't consider or privilege services with a good compromise between parameters, this drawback can be solved by the fuzzification of Pareto dominance in order to rank incomparable services.

The Fuzzy dominance was used in databases community like [20] the authors show the goal of fuzzification of the concept of Pareto dominance and its application in Evolutionary Multiobjectif Optimization. Other works use this principle
and applied it in Genetic or particle Swarm Algorithm. In service computing community, [5] use the fuzzy-dominance and propose the α-dominance to rank Web service based on QoS parameters and associates the fuzzy-dominating score to Web services.

Like mentioned in [20] the measures between two vectors a, b "a dominates b by degree α" and "a is dominated by b to degree α" is not symmetric, In addition to that, in [19] the authors demonstrates that the use of the dominated measure is more efficient in selecting the top-k services than the dominating measure. Our work is close to [5]. However, [5] use fuzzy-dominating relationship to compare the services instead of use fuzzy-dominated measure in ranking services. According to these observations, we define the Fuzzy Dominated relationship Fdet and the Average Fuzzy dominated Score AFDetS(). The next section presents the definition of this concept and its utilization in our context.

# 3 Problem formalization

In this section, we are going to study the fuzzification of the Pareto dominance relation, and show its application on our example (Table1). To allow for a uniform measurement of Web Services, we first normalize the different QoS value in the range [0,1].

## 3.1 Normalization of QoS parameters

let be S a set of similar functionally services $S = S_1, ..., S_n$. Suppose that we have R quantitative $Q_oS$ values for a service $S_i$. we use the vector $Q(S_i) = \{Nq_1(S_i), ..., Nq_r(S_i)\}$ to represent the $Q_oS$ attributes of a service $S_i$ where the function $Nq_k(S_{ij})$ represent the k-th Normalized quality attribute of $S_i$. We convert the negative attributes(time, cost) into positive attributes by multiplying their values by -1 so that the higher value is the higher quality. We normalize the different QoS values in the range [0, 1], as follow :

$$Nq_k(S_i) = \frac{q_k(S_i) - Qmin(q_k)}{Qmax(q_k) - Qmin(q_k)} \quad (1)$$

Where $Nq_k(S_{ij})$ is the normalized QoS value of the Web service $S_{ij}$ on the $QoS$ parameter $q_k$ and $Qmin(q_k)$ (resp. $Qmax(q_k)$ is the minimum (resp. maximum) value of the $QoS$ parameter $q_k$. Table2 shows the QoS values of Web services example of Table 1 after normalization.

## 3.2 Fuzzification of Pareto dominance relation

Services of the same functionality differ only in term of QoS. Like mentioned above, the skyline consists of the set of points which are not pareto dominated by any other.
<table><caption>**Table 2.** Web Services with Normalized QoS</caption><thead><tr><th>Web service</th><th>Nq1</th><th>Nq2</th><th>Nq3</th><th>Nq4</th></tr></thead><tbody><tr><td>s1</td><td>1</td><td>0.74</td><td>1</td><td>0.68</td></tr><tr><td>s2</td><td>0.98</td><td>0</td><td>0.77</td><td>0</td></tr><tr><td>s3</td><td>0.60</td><td>0.92</td><td>0.80</td><td>0.68</td></tr><tr><td>s4</td><td>0</td><td>0.75</td><td>0.98</td><td>1</td></tr><tr><td>s5</td><td>0.79</td><td>1</td><td>0.76</td><td>0.82</td></tr><tr><td>s6</td><td>0.94</td><td>0.74</td><td>0.60</td><td>0.68</td></tr><tr><td>s7</td><td>0.89</td><td>0.62</td><td>0.45</td><td>0.68</td></tr><tr><td>s8</td><td>0.90</td><td>0.59</td><td>0</td><td>0.50</td></tr></tbody></table>

**Definition 1. (Pareto Dominance)**

Let $S_i$ and $S_j$ be two Web services, Given a set of d QOS parameters $Q = \{q_1, ..., q_d\}$, We say that $S_i$ dominates $S_j$ denoted by $S_i \succ S_j$, iff $\forall q_k \in Q$, $q_k(S_i) \ge q_k(S_j)$ and $\exists q_t \in Q, q_t(S_i) > q_t(S_j)$.

Pareto dominance does not differentiate between Web services with good compromise and those with bad compromise, to clarify this, let us return to our example (Table2) and consider $S_4$ and $S_5$, in fact neither $S_4$ dominates $S_5$ nor $S_5$ dominates $S_4$, the two services are incomparable and belong to the skyline because $S_4$ is better than $S_5$ in $q_3$ and $q_4$, and $S_5$ is better than $S_4$ in $q_1$ and $q_2$. However we can consider that $S_5$ is better than $S_4$ since $q_1(S_5) = 0.79$ is much higher than $q_1(S_0) = 0$. In addition to that, $q_3(S_5) = 0.76$ and $q_4(S_5) = 0.82$ are almost close to (respectively) $q_3(S_4) = 0.98$ and $q_4(S_4) = 1$. For this reason, it is interesting to fuzzify the Pareto dominance. The goal of the fuzzification of Pareto dominance is to allow a practically usable numerical comparison between two service and express the extent to which a Web service (more or less) is dominated by another one.

To compute the Fuzzy dominance degrees it's important to distinguish between the measure of two concepts : the dominating score and the dominated Score between two service $S_i$ and $S_j$. The first one express the degree to which $S_i$ dominates $S_j$ and the second express the degree to which $S_i$ is dominated by $S_j$ and the measure of dominance is not symmetric. We will use in our work the concept of dominated relation. We define below the fuzzification of the dominated relation.

**Definition 2. (Fuzzy-Dominated Score)**

let be $S$ a set of functionally similar services, $S_i$ and $S_j \in S$. Let $Q = \{q_1, ..., q_d\}$ be a vector of d QoS parameters.

First we define the monotone comparison function $\mu_{\varepsilon,\lambda}$ to express the degree to which $u$ is dominated by $v$, where $u$ represent $q_k(s_i)$ and $v$ represent $q_k(s_j)$ as follow:

$$ \mu_{\varepsilon,\lambda}(u,v) = \begin{cases} 0 & \text{if } (u-v) \ge \varepsilon \\ |u-v-\varepsilon|/|\lambda+\varepsilon| & \text{if } \lambda+\varepsilon \le (u-v) < \varepsilon \\ 1 & \text{if } (u-v) < \lambda+\varepsilon \end{cases} \quad (2) $$
Where $\varepsilon, \lambda \in [-1, 0], \varepsilon + \lambda \ge -1$

Then, we define the Fuzzy-Dominated score $FDet(S_i, S_j)$ to express the degree to which $S_i$ is dominated by $S_j$ as follows:

$$FDet(s_i, s_j) = \frac{1}{d} \sum_{k=1}^{d} \mu_{\lambda, \varepsilon}(q_k(s_i), q_k(s_j)) \quad (3)$$

Let us reconsider our example and compare Web services $S_4$ and $S_5$ by using $FDet()$, with $\varepsilon = -0.1$ and $\lambda = -0.2$ we have $FDet(S_4, S_5) = 0.5$ and $FDet(S_5, S_4) = 0$ this means that $S_5$ is not fuzzy dominated by $S_4$ and is little more better than $S_4$. This concept gives a good compromise between $QoS$. In fact, this is more expressing than $S_4$ and $S_5$ not comparable by Pareto dominance. In what follows, we use the $FDet()$ to rank Web services.

**Definition 3.** (Averaged-Fuzzy-Dominated-Score)

In order to rank a Web service $S_i$ in its class $S$, we first, make pairwise comparison with the other services and associate it a score by:

$$AFDetS(S_i) = \frac{1}{|S| - 1} \sum_{j=1, i \neq j}^{n} FDet(S_i, S_j) \quad (4)$$

Then, we retain service with lower $AFDetS()$ on a higher ranking position.

The Table3 shows the services of our example (Table 1) after computing $AFDetS$ score and ranking with $\varepsilon = 0$ and $\lambda = -0.2$.

<table><caption>**Table 3.** Services'Rank according to $AFDetS()$</caption><thead><tr><th>Rank</th><th>Web service</th><th>AFDedS()</th><th>Nq1</th><th>Nq2</th><th>Nq3</th><th>Nq4</th></tr></thead><tbody><tr><td>s1</td><td></td><td>0,071</td><td>1</td><td>0,74</td><td>1</td><td>0,68</td></tr><tr><td>s5</td><td></td><td>0,107</td><td>0,79</td><td>1</td><td>0,76</td><td>0,82</td></tr><tr><td>s6</td><td></td><td>0,143</td><td>0,94</td><td>0,74</td><td>0,60</td><td>0,68</td></tr><tr><td>s3</td><td></td><td>0,25</td><td>0,60</td><td>0,92</td><td>0,80</td><td>0,68</td></tr><tr><td>s7</td><td></td><td>0,286</td><td>0,89</td><td>0,62</td><td>0,45</td><td>0,68</td></tr><tr><td>s4</td><td></td><td>0,312</td><td>0</td><td>0,75</td><td>0,98</td><td>1</td></tr><tr><td>s8</td><td></td><td>0,393</td><td>0,90</td><td>0,59</td><td>0</td><td>0,50</td></tr><tr><td>s2</td><td></td><td>0,571</td><td>0,98</td><td>0</td><td>0,77</td><td>0</td></tr></tbody></table>

We can observe that the top service is $S_1$ which is better than the others in $q_1$, $q_2$ and has a good value in the other $QoS$ parameters. We remark that services that have some $QoS = 0$ are at the bottom of the ranking. Let us consider $S_6$ and $S_4$, according to the result provided by Pareto dominance $S_4$ belong to the skyline, but $S_6$ does not, however $S_4$ have the worst response time($q_1$)) and $S_6$ has a good compromise between $QoS$ parameters. According to (Table3: Fuzzy-Dominated Score)$S_4$ was downgraded to the Rank 7. On the other hand, the
Service $S_6$ which has a good compromise between $QoS$ parameters was set up to the 3rd rank.

From this result, we confirm that the use of $Fed()$ can give more interesting results in terms of balanced of $QoS$ than the other approaches.

# 4 Experimental Evaluation

In order to evaluate and prove the effectiveness of our approach, we compare the result of using Fuzzy-Dominated with the Fuzzy-Dominating score. For this purpose, we implement the function fuzzy-dominating proposed in [6] and termed it *AFDingS* and compare it to our Approach *AFDetS*. All the experiments are conducted on the same software and hardware, which were Intel i3-2365M CPU @ 1.40GHz 4 processors, 4.0GB of RAM, Ubuntu 13.10, Netbeans 7.4. Several simulations have been made by varying the parameters:

- $ε, λ$,

- *d*:number of $QoS$ parameter,

- *n*:number of services of the same class *S*.

For each simulation we take the *Top-5* services generated by the algorithms *AFDingS* and *AFDingS* and compare them. Different Services' subsets were taken from the real *QoS* dataset provided by [23]. The dataset includes informations about 2507 real-world web services. Each service comprise measurement of nine *QoS* parameters. The service name and its WSDL address are also included in the dataset. We group functionally similar Services into clusters, for example the cluster "sms" (sending sms) contains 30 real services. The cluster "search"(ie. Search Engine Web services such as Google Search, Amazone, etc.) contain 92 services.

**a-Varying ε and λ:** We present below two scenarios (Table4) and (Table5) by varying $ε$ and $λ$ on a set of 30 services belonging to the class SMS. Each service has 4 $QoS$ parameters.

<table><caption>**Table 4.** Top-5 Services Rank according to *AFDingS*, *AFDetS*() with $ε = 0, λ = -0.2$</caption><thead><tr><th colspan="3">Top-5 AFDingS</th><th colspan="2">Top-5 AFDetS</th></tr><tr><th>Si</th><th>AFDingS</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>, q<sub>4</sub>)</th><th>Si</th><th>AFDetS</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>, q<sub>4</sub>)</th></tr></thead><tbody><tr><td>S5</td><td>0.566</td><td>[0.787, 1.0, 0.758, 0.818]</td><td>S12</td><td>0.071</td><td>[1.0, 0.738, 1.0, 0.682]</td></tr><tr><td>S4</td><td>0.551</td><td>[0.0, 0.754, 0.975, 1.0]</td><td>S5</td><td>0.107</td><td>[0.787, 1.0, 0.758, 0.818]</td></tr><tr><td>S12</td><td>0.529</td><td>[1.0, 0.738, 1.0, 0.682]</td><td>S6</td><td>0.143</td><td>[0.941, 0.738, 0.603, 0.682]</td></tr><tr><td>S30</td><td>0.423</td><td>[0.6, 0.918, 0.797, 0.682]</td><td>S30</td><td>0.25</td><td>[0.6, 0.918, 0.797, 0.682]</td></tr><tr><td>S6</td><td>0.329</td><td>[0.941, 0.738, 0.603, 0.682]</td><td>S7</td><td>0.286</td><td>[0.0, 0.754, 0.975, 1.0]</td></tr></tbody></table>
<table><caption>**Table 5.** Top-5 Services according to *AFDingS*, *AFDetS*() with $\varepsilon = -0.1$, $\lambda = -0.2$</caption><thead><tr><th colspan="3">Top-5 AFDingS</th><th colspan="2">Top-5 AFDetS</th></tr><tr><th>Si</th><th>AFDingS</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>, q<sub>4</sub>)</th><th>Si</th><th>AFDetS</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>, q<sub>4</sub>)</th></tr></thead><tbody><tr><td>S4</td><td>0.443</td><td>[0.0, 0.754, 0.975, 1.0]</td><td>S5</td><td>0.0</td><td>[0.787, 1.0, 0.758, 0.818]</td></tr><tr><td>S5</td><td>0.421</td><td>[0.787, 1.0, 0.758, 0.818]</td><td>S12</td><td>0.036</td><td>[1.0, 0.738, 1.0, 0.682]</td></tr><tr><td>S12</td><td>0.036</td><td>[1.0, 0.738, 1.0, 0.682]</td><td>S6</td><td>0.107</td><td>[0.941, 0.738, 0.603, 0.682]</td></tr><tr><td>S30</td><td>0.321</td><td>[0.6, 0.918, 0.797, 0.682]</td><td>S30</td><td>0.143</td><td>[0.6, 0.918, 0.797, 0.682]</td></tr><tr><td>S6</td><td>0.223</td><td>[0.941, 0.738, 0.603, 0.682]</td><td>S7</td><td>0.25</td><td>[0.892, 0.623, 0.453, 0.682]</td></tr></tbody></table>

We can observe from the results on (Table 4) and (Table 5) that the ranking given by *AFDetS* is more interesting than the one given by *AFDingS* even if we vary $\varepsilon$ and $\lambda$ the top-1 is always better according to *AFDetS*. The service S4 (Table 5) is the top-1 according to *AFDing* while it does not belong to the top-5 according to *AFDetS* because of its bad first criterion value. We can say that *AFDetS* favors services with good value in all parameters and discards services with worst values in some *QoS* parameters even if the others are good.

**b-Varying d and n:** We present below two scenarios by varying *d* from 7 to 9 on a set of 92 services belonging to the class search. We fixed $\varepsilon = -0.1$ and $\lambda = -0.2$. The result of the top-5 services provided by *AFDingS* and *AFDetS* approach are shown in (Table 6) and (Table 7).

<table><caption>**Table 6.** Top-5 Services(*AFDingS*() Vs. *AFDetS*()) with *d* = 7</caption><thead><tr><th></th><th>Si Score</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>, q<sub>4</sub>, q<sub>5</sub>, q<sub>6</sub>, q<sub>7</sub>)</th></tr></thead><tbody><tr><td rowspan="5">AFDingS</td><td>S70</td><td>0.409 [0.183, 0.904, 0.618, 0.964, 0.767, 1, 0.815]</td></tr><tr><td>S30</td><td>0.388 [0.164, 0.904, 1, 0.964, 0.767, 1, 0.815]</td></tr><tr><td>S24</td><td>0.385 [0.005, 1, 0.829, 1, 0.767, 1, 0.667]</td></tr><tr><td>S72</td><td>0.381 [0.474, 0.795, 0.260, 0.807, 0.767, 0.667, 0.815]</td></tr><tr><td>S16</td><td>0.365 [0.003, 1, 0.419, 1, 1, 0.667, 0.111]</td></tr><tr><td rowspan="5">AFDetS</td><td>S30</td><td>0.005 [0.164, 0.904, 1, 0.964, 0.767, 1, 0.815]</td></tr><tr><td>S52</td><td>0.006 [0.016, 0.819, 0.955, 0.94, 0.767, 1, 0.667]</td></tr><tr><td>S24</td><td>0.006 [0.005, 1, 0.829, 1, 0.767, 1, 0.667]</td></tr><tr><td>S70</td><td>0.008 [0.183, 0.904, 0.618, 0.964, 0.767, 1, 0.815]</td></tr><tr><td>S45</td><td>0.022 [0.042, 0.831, 0.382, 0.940, 0.767, 1, 0.667]</td></tr></tbody></table>

From (Table 6), we can observe that the ranking given by *AFDetS* is more interesting than the one given by *AFDingS*. The top-1(*AFDetS*) is the service S30. This latter has better value than the top-1(*AFDingS*) on *q*<sub>3</sub>. Moreover, service S30 is close to service S7 on *q*<sub>1</sub> parameter. We can remark that the service S16 is included into top-5(*AFDingS*) while it does not belong to the
<table><caption>**Table 7.** Top-5 Services($AFDingS$() Vs. $AFDetS$()) with $d = 9$</caption><thead><tr><th></th><th>Si Score</th><th>Qos(q<sub>1</sub>, q<sub>2</sub>, q<sub>3</sub>q<sub>4</sub>, q<sub>5</sub>, q<sub>6</sub>, q<sub>7</sub>, q<sub>8</sub>, q<sub>9</sub>)</th></tr></thead><tbody><tr><td rowspan="5">AFDings</td><td>S24 0.397 [0.050, 1, 0.829, 1, 0.767, 1, 0.667, 0.004, 0.958]</td></tr><tr><td>S16 0.366 [0.003, 1, 0.419, 1, 1, 0.667, 0.111, 0.030, 0.358]</td></tr><tr><td>S60 0.344 [0.016, 0.988, 0.955, 1, 0.333, 1, 0.259, 0.008, 0.337]</td></tr><tr><td>S55 0.328 [0.179, 0.916, 0.244, 0.976, 0.767, 1, 0.815, 0.066, 0.800]</td></tr><tr><td>S70 0.318 [0.183, 0.904, 0.618, 0.964, 0.767, 1, 0.815, 0, 0.021]</td></tr><tr><td rowspan="5">AFDetS</td><td>S24 0.006 [0.050, 1, 0.829, 1, 0.767, 1, 0.667, 0.004, 0.958]</td></tr><tr><td>S45 0.018 [0.042, 0.831, 0.382, 0.940, 0.767, 1, 0.667, 0.030, 0.937]</td></tr><tr><td>S55 0.018 [0.179, 0.916, 0.244, 0.976, 0.767, 1, 0.815, 0.066, 0.800]</td></tr><tr><td>S52 0.024 [0.016, 0.819, 0.955, 0.940, 0.767, 1, 0.667, 0.017, 0.105]</td></tr><tr><td>S30 0.027 [0.064, 0.904, 1, 0.964, 0.767, 1, 0.815, 0.092, 0.053]</td></tr></tbody></table>

top-5($AFDetS$) because of its bad values on $q_3$ and $q_7$. In fact, it is replaced by service S45 which has a good compromise between its $QoS$ parameters.

Let us consider now the ranking with $d = 9$ (Table 7). The two ranking methods have the same top-1 (service S24). However, the other services given by $AFDetS$ are different from those provided by $AFDingS$. The service S16 and the service S70 which belong to (top-5($AFDingS$)) are discarded by $AFDetS$ from the top-5 because they contains some bad values (close /or equal to 0) on some $Qos$ criteria. This two services are replaced by respectively the service S45 and the service S30 by the $AFDetS$ approach, we can remark that these two services present a good compromise between their $QoS$ parameters.

## 5 conclusion

In this paper, we have presented an approach for ranking $QoS$-based-Web services. We have presented a fuzzification of the Pareto-dominance and introduced the concept $AFDetS$ which associates a score to a service according to the Fuzzy dominated relation. We demonstrate that the fuzzy dominated concept can offer an alternative to compare services when they are non comparable with pareto dominance. Experimental results show that the proposed approach is effective in comparison with the Fuzzy Dominating ranking. For future work, we can use this concept for the web service composition.

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