Novel Approach for Computing Skyline Services with Fuzzy

Consistent Model for QoS- based Service Composition

Fatma Rhimi, Saloua Ben Yahia and Samir Ben Ahmed

Faculty of Sciences LISI-INSAT, University of Carthage, Tunis, Tunisia

Keywords: Fuzzy Logic, Optimization, Skyline, Web Services Composition.

Abstract: Service composition is emerging as an effective solution to ensure the integration of multiple atomic web

services in order to create value-added customized services. However, the exploding number of the

deployed service candidates that is constantly increasing makes the process of choosing the best service

candidates an important challenge. When there are multiple web services that offer the same functionalities,

we need to select the best one according to its non-functional criteria (e.g. response time, price, reliability).

Skyline is a technique that helps reducing the size of our search space and comes as a complementary

approach to the optimization methods. In fact, Skyline consists in preselecting the best candidates in the

search space according to their non-functional criteria. Those web services are considered optimal as they

are not dominated by any other point in the search space. Therefore, we will eliminate all the irrelevant web

services which will considerably reduce the complexity of the computation. Most of the current Skyline

computation relies on a strict dominance relationship called Pareto-dominance. In this paper, we propose a

new method to compute the Skyline points with a fuzzy approach which allows taking into consideration the

users preferences. We will through this paper show how we could construct a consistent fuzzy model to

overcome the shortcomings of web service composition computation. A detailed study of the approach will

demonstrate the effectiveness and the efficiency of the proposed algorithm.

1 INTRODUCTION

Web services are software components designed to

enhance the interoperability for machine-to-machine

interaction among different applications and

different platforms. This is why business structures

are moving today towards the service-oriented

architecture as web services seem to be the best

solution to allow the exchanges between them.

Service composition is a process that combines

multiple atomic web services in order to create

value-added web services. Hence, it is arising as an

effective solution to deliver customised services to

the different users.

However, today with the prevalence of

paradigms such as Cloud Computing and XAAS

(everything as a service) that provide services on

demand, the number of available web services had

exploded. This is why it has become difficult to

choose the best candidates that would ensure an

optimal composition.

Quality-of-Service (QoS) is widely employed to

represent the non-functional characteristics of Web

services and has been considered as the key factor in

service selection. QoS is defined as a set of

properties including response time, throughput,

availability, reputation, etc. Hence, optimal

composition can be defined as the composition that

corresponds the most to the constraints provided by

the end user in terms of non functional criteria.

The problem of QoS-based service composition

becomes especially important as the number of

candidate web services increases enormously every

single day. Hence, performing an exhaustive search

to find the best composition is not efficient in this

case. In fact, even with hundreds of candidates the

time execution of exhaustive algorithms is already

very high and exceeds the time execution constraints

as the number of possible combinations is very

large. To tackle this problem, many researchers used

methods such as Linear Programming methods

which are proved to be very effective in a small

space. However, today with the proliferation of the

web technologies, there are multiple service

providers who offer web services with the same

functionality but with different QoS attributes.

Those methods have an exponential cost in a context

where the number of service candidates is large as

135

Rhimi F., Ben Yahia S. and Samir B..

Novel Approach for Computing Skyline Services with Fuzzy Consistent Model for QoS- based Service Composition.

DOI: 10.5220/0005499901350143

In Proceedings of the 10th International Conference on Software Paradigm Trends (ICSOFT-PT-2015), pages 135-143

ISBN: 978-989-758-115-1

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

the number of possible combinations grows

exponentially.

Skyline is a technique that comes as a solution

that helps reducing the search space based on a

dominance relationship to preselect the best services

and prune the others. Intuitively, a skyline query

selects the “best” or most “interesting” points with

respect to all dimensions. In this work, we define

and exploit dominance relationships between

services based on their QoS attributes. This is used

to identify services in a service class that are

dominated by other services in the same class

. Most

of the researchers addressed the Skyline with a

Pareto dominance relationship: a service p

dominates another service q if p is at least as good as

q in all the dimensions and strictly better in at least

one dimension. However, such strict dominance

relationships privileges web services with some bad

and some good attributes. Besides, in real world, the

user’s preferences are usually complex and vague. It

might be difficult to require a business user to

express a crisp preference for an item or a feature of

an item, and it is therefore difficult to represent the

user‘s preferences with crisp numbers. In this study,

fuzzy set techniques are used to describe user’s

complex and vague preferences. We will through

this paper address the Skyline based on a fuzzy

dominance relationship which is a known to be a

more flexible relationship.

1.1 Contributions

This paper aims to present a new approach for

computing Skyline services in order to reduce the

number of candidates. We suggest preselecting the

best services based on fuzzy dominance

relationships.

Fuzzy sets are more suited to the expression and

the interpretation of the user’s preferences. Usually

users use terms such as ‘rather

fast’, ‘not expensive’, ‘quite reliable’ to express

their preferences. Besides, fuzzy sets can select

service Skyline with a compromise between good

and bad attributes as they use a more flexible

dominance relationship.

However, unlike Pareto dominance relationship,

dominance relationship of fuzzy sets does not

preserve the transitivity property. Pruning services

without checking this property can lead to erroneous

results. Hence, constructing a consistent fuzzy

model is crucial for the effectiveness of the

computation. Furthermore, checking the dominance

relationship between each pair of services is

computationally expensive. So, using structures as

R-tree may be very effective for reducing the cost of

computation.

Considering all this, our main contributions may

be summarized in the following:

- We will address the problem of computing

service Skyline with a consideration of

user’s preferences by making use of fuzzy

preference relationships rather than Pareto

dominance relationships.

- We introduce a novel approach to compute

the service Skyline that consists in a two-

phase algorithm: a transformation phase

which constructs a consistent fuzzy model

from the collected data and a computing

phase which determines the dominance

relationship with a branch-and-bound

algorithm.

- We evaluate the efficiency and the

effectiveness of the proposed method with

a theoretical study and we will leave the

experimental study for the future work.

1.2 Outline

Section 2 presents the related work of the web

services composition problem, the Skyline

techniques and fuzzy techniques. In sections 3 we

will define the problem statement of our research

and present the background of this work with a

remainder of the concept of Skyline and fuzzy sets

so we can advance the followed approach. Sections

4 and 5 will describe the different steps of the

proposed approach. Section 6 contains an

experimental study for the approach to evaluate the

results. Finally, we will conclude the paper and give

an overview on our future work.

2 RELATED WORK

The problem of QoS-based web service selection

and composition has received a lot of attention

during the last years. Local selection methods using

techniques such as Simple Additive Weighting

(SAW) were conducted to select services that ensure

an optimal composition. However, local selection

could not satisfy global constraints on the

composition as it treats each service class

individually. Zeng et al. (2003) tackled this problem

using a global planning composition based on mixed

integer Programming technique for dynamic and

quality-driven selection. However, the costs of this

approach are exponential in a large space. Linear

programming methods are very effective when the

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size of the problem is small, but suffer from poor

scalability due to the exponential time complexity of

the applied search algorithms. In their work, Alrifai

and Risse (2009) proposed a hybrid selection

approach that combines local selection with global

selection by decomposing global constraints into

local constraints in order to find close-to optimal

solutions. Canfora (2005) proposed a genetic

algorithm to the QoS-based composition. Genetic

algorithms are based on the evolution theory and in

opposition to linear programming algorithms, the

input data doesn’t need to be linear. Besides, genetic

algorithms are related to the number of service

classes and not to the number of candidate web

services, so they are more effective in a large space

context. However, linear programming is proved to

be faster than genetic algorithms and is preferred

hence in a small space. Yu and Keiw-Jay (2004)

proposed heuristic algorithms that can come as an

alternative to exact solutions. The authors modelled

the problem as combinatorial problem and proposed

a heuristic Branch and Bound algorithm (WS HEU)

and a heuristic graph model (MCSP-K). The two

algorithms are proved to be more efficient than exact

algorithms. Ardagna and Pernici (2007) tried to

overcome the shortcomings of both local and global

service composition by proposing an approach that

addresses optimization problems under severe QoS

constraints.

However, today, as we are moving from limited

data systems to large scale systems, the methods

proposed above are no longer practical. Cloud-based

composition approaches were developed to deal with

the problem of QoS-based web services composition

in large scale systems. One can classify those

approaches into five categories: classic approaches

such as the work of Kofler, Haq and Schikuta (2010)

where the authors tried To achieve a feasible

concrete workflow for service composition with

respect to the consumer QoS requirement, the

problem is considered to be equivalent to a multi-

dimensional multi-choice knapsack problem

(MMKP) in which a parameter called happiness that

is calculated based on QoS parameters is used as the

utility function. Combinatorial approaches such as

the works of Ludwig (2011) where in the service

provider system an improved genetic algorithm is

proposed; Yang, Mi and Sun (2012) and Ye where

game theory is used to propose a service level

agreement (SLA)-based service composition

algorithm., Zhou and Bouguettaya (2011)

where

authors also applied a genetic algorithm to solve the

composition problem in which a roulette wheel

selection algorithm is used to select chromosomes to

execute a crossover operation, framework based

approaches like Pham et al. (2010) who proposed a

new framework for service composition in which a

composition agent is responsible for receiving the

request and providing service management, machine

based approaches with contributions such as the

work of Baou and Dou (2012) researchers designed

finite state machines to consider service correlations

and finally structure based approaches such as the

contribution of Wittern and Menzel( 2012) where

the composition problem is represented by a

directed graph in which the nodes play service roles

and the edges denote the relations between service.

Skyline technique is complementary to these

solutions as it can be used as a pre-processing step to

prune non-interesting candidate services and hence

reduce the computation time of the applied selection

algorithm. The analysis of the Skyline was originally

considered as a mathematical problem. It was then

introduced in the first place in the field of database

by Borzsonyi, Kossmann and Stocker (2001). Given

a set of points in d-dimensional space, the Skyline is

defined as the subset containing the points which are

not dominated by another point. Paradigms like

Block Nested Loops (BNL) and Divide to Conquer

are among the first attempts to solve the computing

of Skyline.The index structures such as B-trees have

also been utilized to improve the performance of

analyzing the Skyline. Nearest Neighbour (NN) and

Branch and Bound Skyline (BBS) are two

representative algorithms that can progressively

address the Skyline based on R-tree structure.

In recent works, many researchers focused on

computing skyline services in the context of service

composition. However, the majority of these works

relied on Pareto dominance relationship for this

purpose Alrifai, Skoutas and Risse (2010), Chen

(2014), Abourezk and Idrissi (2014). Pareto

dominance has the shortcoming of neglecting the

smoothness and fuzziness of human preferences. A

definition and an example of Pareto dominance is

given further in our work. Bouguettaya et al. (2013)

addressed the problem of uncertainty in service

composition and defined a concept called p-

dominant service skyline.

Fuzzy logic was addressed in the optimization

techniques for service composition in many

contributions such as those of Almulla, Almatori and

Yahyaoui (2010), Torres, Astudillo and Salas

(2011), Ping et al. (2006), Xuan and Tsuji (2008).

However, in all these works, fuzzy techniques were

used to find global optimization solutions for web

services selection. Only few works used fuzzy logic

for Skyline computation. To the best of our

NovelApproachforComputingSkylineServiceswithFuzzyConsistentModelforQoS-basedServiceComposition

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knowledge, the work that follows a similar line is

the work of Benouaret et al. (2011) where the

authors defined a concept called the α-dominant

service skyline. However, to overcome the

shortcomings of fuzzy relationships, they proceed in

double-checking the services which is very time-

consuming and complex especially when the search

space is very large. We suggest in this work another

approach for computing skyline with fuzzy

dominance relationship by constructing a consistent

fuzzy model. The consistent fuzzy model allows a

direct pruning of the irrelevant services in the search

space, which will enormously reduce the complexity

of computation. A detailed study is given in the rest

of the paper.

3 BACKGROUND

3.1 Skyline Computation

Skyline can be formally defined as follows:

Given a set of points S in a space with D

dimensions, Skyline points are the points who are

not dominated by any other point in the search space

according to those dimensions. A definition of the

dominance concept is then crucial to the

understanding of the skyline concept.

Pareto dominance

Definition

Given

d the number of dimensions in the space and

two web services in the space, we say that

dominates

denoted by

s

iff

is at least as

good as

in all the dimensions and strictly better

in at least one dimension.

In the literature, many researchers made use of

this concept to compute the service Skyline. In their

work, Alrifai et al. (2010) used the Pareto

dominance to reduce the size of the search space.

They extended their work to compute the set of

representative skyline in the case where the size of

the initial set is still too large. Yu and Bouguettaya

(2011) also used Pareto dominance to introduce a

concept of C-Sky which computes the overall

Skyline of the composition by a combination of the

Skyline sets of individual service classes. Although

those contributions are efficient and effective, their

reliance on Pareto dominance presents some

shortcomings. Pareto dominance is a strict

dominance relationship that privileges services with

good and bad attributes. Besides, it might neglect

user’s preferences. The example below illustrates

this.

Illustrative Example

Let’s consider the common example in the literature

that selects the set of interesting hotels in a

reservation service represented in Fig.2. The hotels

are represented by two criteria: their prices and their

distances from the beach. It is obvious that a hotel

with a low price and a small distance from the beach

is preferred in this case. According to this, the

Skyline points are

,al

and

as they are the only

points that are not dominated by any other point in

the search space.

One can notice that selecting Skyline points with

a Pareto dominance relationship is strict and can

discard potentially good candidates. Let’s consider

for example the point

h (4, 3): According to the

Pareto dominance, this point is dominated by other

points in the space so it is discarded from the

Skyline set. However, some users who accord an

importance to the price would prefer the point

over the point

which has a small distance from

the beach but has a high price (1, 9).

Figure 1: Example of Skyline dataset.

Fuzzy dominance relationships can overcome this

problem as they express the user’s preferences

gradually. The next section will demonstrate this

affirmation

Fuzzy dominance

Given two points in a space with

d dimensions, we

can define the dominance relationship as follows:

(((),())

deg ( )

qsqs















(1)

With:

d : The space dimensions (i.e. the QoS attributes in

our context)

: two points in the search space

(), ( )

mi m j

qsqs

: The values of the

attribute for

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and

respectively.







: A fuzzy membership function that is defined

as follows:

0 if x-y

(, ) 1 if x-y +

otherwise



























(2)

With



0



0.

Let’s for example consider





and

0.3





This would result in

0,0.3

(a, h) 0.5





and

0,0.3

(h, a) 0.5





. Hence, point h would not be

discarded which proves that fuzzy dominance

privileges points with good compromise.

In this paper, we will propose an approach for

computing Skyline with fuzzy dominance. The next

section will be a remainder of the basics of fuzzy

logic and fuzzy sets that are crucial to the

understanding of the rest of the paper.

3.2 Fuzzy Sets

Fuzzy sets were introduced by Lotfi Zadeh A.

(1965) as an extension of the classical notion of sets.

Fuzzy sets are described by means of a membership

of a real value in the interval [0, 1] function. Fuzzy

sets generalize classical sets, since the indicator

functions of classical sets are special cases of the

membership functions of fuzzy sets, if they do not

take the values 0 or 1. The theory of fuzzy sets can

be used in a wide range of areas in which

information is incomplete or inaccurate.

Furthermore, they are well suited for expressing non

exact linguistic terms such as ‘rather reliable’,

‘cheap’ and ‘not expensive’ that are widely used by

web services users.

Binary fuzzy relation between two non-empty fuzzy

sets is a fuzzy subset of the Cartesian product



namely:

{,, (,): , }RxyUxyxXyY



Where





:0,1UXY

 is a membership

function which assigns to each pair ,

Xy Y

the membership degree

(, )Uxy

, interpreted as the

degree of the relation between ,

Xy Y.

(, ) 1Uxy

 means that the two components x and

y are fully connected.

(, ) 0Uxy

 means that the

two elements are completely independent.

Definitions

Fuzzy preference relationships

A fuzzy preference relation P on a set of alternatives

X is a fuzzy set on the product X × X that is

characterized by a membership function





:0,1uXX

 . The fuzzy relation can be

represented by the matrix

NN ()pp

 with

(, )puxx

ij i j



,1..ij n



is interpreted as the degree of preference of

over



indicates indifference of

preference between the alternatives, 1P



interpreted as

is totally preferred to

and

 is interpreted as

is preferred to x .

Hence we have

0.5P



Fuzzy preference relationships are assumed to be

additively reciprocal which implies that

1pp

ij ji



 .

Additive transitivity

Additive transitivity for fuzzy preference relations

can be seen as a property to characterize consistency

in the case of fuzzy preference relations. The

mathematical formulation of the additive transitivity

was given by Tanino (1988).

(0.5)( 0.5)( 0.5)p p p i, j,k {1,...,n}

jk ik



 (3)

This equation can be written as follows:

P+P +P

jk ik



ijk  (4)

4 CONSISTENCY OF FUZZY

MODELS

In decision making, the study of consistency when

the decision makers express their opinions by means

of preference relations becomes a very important

aspect in order to avoid misleading solutions. In

decision making problems based on fuzzy

preference relations the study of consistency is

associated with the study of the transitivity property.

The decision-making process with preferences is

based on fuzzy preference relationships, where the

process is related to a degree of preference of an

NovelApproachforComputingSkylineServiceswithFuzzyConsistentModelforQoS-basedServiceComposition

139

alternative over another. Therefore, establishing

properties to check for preference relations is very

important for the design of valid models for the

decision making process. One of these properties is

called the consistency property. The lack of

consistency in decision making can lead to

incoherent conclusions; this is why it is important, if

not essential, to study the conditions under which

consistency is satisfied. Transitivity is one of the

most important properties concerning preferences. In

a fuzzy context, where a user expresses his opinions

using fuzzy preference relations, a traditional

requirement to characterize consistency is using

transitivity, in the sense that if an alternative

preferred to alternative

and this one to x

then

alternative

should be preferred to x

Our approach consists in generating a preference

fuzzy model comprising n-1 preference values

collected from users and generated from a

membership function. This model will respect the

properties of reciprocity and transitivity. Our idea is

that by constructing a consistent model from the

start we can reduce the time cost of the checking

process in the Branch and Bound Skyline with fuzzy

dominance relationship. In fact, without preservation

of consistency, the pruning of irrelevant services can

be direct as a service can be in the same time

dominating and dominated by a service. To

overcome this problem, we suggest injecting the

transitivity property from the beginning, when

collecting the preference values from the users, by

applying a set of transformations and operations on

fuzzy sets.

Herrera et al. (2004) chose the additive

transitivity for the construction of the consistent

model. A fuzzy preference model is consistent if and

only if it fulfills Eq. (3).

This leads to establish the following result:

...

( 1) ( 1)( 2) ( 1)

pp p p

ii i i j i





 

(5)

The proof of this affirmation is found in their work.

For sake of simplicity, we will only use the result of

this proof in the rest of the paper. This property

allows us to construct the

1n 

preference values

12 23 (n 1) n

, ,...,pp p



collected from the users with a

fuzzy relationship function.

According to the definitions above, these two

matrices are additively transitive; hence the fuzzy

model is consistent. It is worth to notice that in

certain cases, we would have obtained a matrix P

with entries not in the interval [0, 1], but in an

interval [−a, 1 + a], being a > 0. In such a case, we

would need to transform the obtained values using a

transformation function which preserves reciprocity

and additive consistency. Herrera et al. (2004)

proposed the following function for normalizing the

values:

f(x)







(6)

Where Eq. (6) is a function verifying the following

properties:



(a) 0

(1 a) a

() (1 ) 1 a,1 a

a,1 a

fx f x x

f(x) + f(y) + f(z) = , x, y, z











 

uch that x + y + z =

Hence, we can summarize the method to construct a

consistent fuzzy model from the

1n 

preference

values collected in the following steps:

Compute the set of preference values A with (1)

such as:

{, }

ij ij ii+1 i+1i+2 j-1j

j - i + 1

p p = - p - p . . . - p i j





Compute the overall preference relationship

matrix P. As P is reciprocal we will have:

{ , ..., } {1 ,1 ...,1 }

12 23 1 12 23 1

pA A p p p p p p

nn nn

   





3. Determine the range for the normalization :

12 23 1

a = | { , ..., }}|

min{B p p p







1. Compute the normalized preference relationship

matrix such as:



a,1 a 0,1

p' = f(p) with

f(x)









5 SKYLINE USING A BRANCH

AND BOUND ALGORITHM

WITH A CONSISTENT FUZZY

MODEL

5.1 Branch and Bound Skyline using

Pareto Dominance Relationship

Branch and Bound Skyline was first introduced by

Papadias (2003) for the computation of Skyline

points with a Pareto dominance relationship. Branch

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and Bound Skyline is an algorithm based on R-Tree

structure known for its efficiency and effectiveness

in large spaces. It is widely used to reduce the search

space. An example of R-Tree data is illustrated in

Fig.2: Data points are regrouped in nodes according

to their distance from the origin. An entry is the

Minimum Bound Rectangle of a node and a leaf

entry is a data point. Papadias used a Pareto

dominance relationship to determine the Skyline

points in the search space. In Pareto dominance, the

property of transitivity is verified. However, this

property is not verified by the fuzzy dominance

relationship. When transitivity is not preserved,

discarding some points can lead to erroneous results.

Thus, constructing a consistent fuzzy model with

transitivity property is crucial for establishing

correct results. Benouaret, Benslimane and Hadjali

(2011) used the Branch and Bound Skyline with a

fuzzy dominance membership function. In order to

address the above problem, they developed an

optimization technique called

a - dominant

service

Skyline. This new concept is proved to be effective

and efficient. However, the authors only considered

the lack of antisymmetry in the fuzzy relationships.

They double-check every point in the heap for

dominance before inserting it in the Skyline. Our

proposed algorithm comes as a solution to this

problem. We suggest constructing form the collected

data a consistent fuzzy model by applying fuzzy

transformations. This model will preserve the

transitivity property. Hence, the pruning process can

be direct and we will be sure that the results are not

erroneous.

5.2 Branch and Bound Algorithm with

Fuzzy Dominance Relationship

The proposed algorithm is a two-phase algorithm.

The first phase consists in transforming the data

Figure 2: Example of R-Tree.

points of the search space into a consistent fuzzy

model. The second step is determining the Skyline

points with a Branch and Bound algorithm according

to the fuzzy dominance relationship.

orithm 1: Fuzzy Consistent Branch and

Bound Sk

line

Input: service R-Tree, fuzzy membership

function

Output: set of Skyline points

Begin

1. Heap H=Ø, Skyline S=Ø

2. For all the services in the search

space inserted in the R-Tree:

3. Compute the dominance degree for all

the QoS criteria of each pair of services

inserted in the R-tree according to Eq.

(1) and store them in the R-Tree

4. Transform the computed values

according to Eq. (5).

5. Determine the value of the

normalization range

6. Compute the overall normalized

values according to Eq. (6).

7.For all entries in the Root:

8. Insert all entries in the heap

9. While heap not empty

s 10. Remove the entry e with the min

distance

11. If e is fuzzy-dominated by a

point in S discard e

12. Else

13. if e is an intermediate

entry

14. For each child c of e

15.If c is not fuzzy-

dominated by some point in S Insert c into

heap

16. Else Insert c into S

17. End while

End FCBB

6 EXPERIMENTAL

EVALUATION

In this section we verify the effectiveness and

efficiency of our proposed algorithm referred to as

CFBBS (Consistent Fuzzy Branch and Bound

Skyline). We conduct a set of experiments by

comparing our algorithm to a Branch and Bound

Skyline algorithm with Pareto dominance

relationship referred to as PDBBS. In this

experiment we will focus on the size of the service

NovelApproachforComputingSkylineServiceswithFuzzyConsistentModelforQoS-basedServiceComposition

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Skyline provided by both algorithms in order to

study how the fuzzy dominance affects the selected

Skyline points. Then, to study the scalability of our

algorithm, we developed a native approach for

skyline computation referred to as NA. We took in

this study into consideration the effects of the

number of services. Other parameters will be studied

on future work. The parameters are summarized in

Table1. The algorithms were implemented in Java.

The experiments were conducted on a 2.00 GHz

Intel core I7 CPU and 8 GB of RAM, running

Windows.

6.1 Size of the Skyline

Figure 3: Effect of the number of dimensions on the

Skyline size.

Figure 4: Effect of the number of services on the Skyline

size.

Figure 3 shows that the size of the Skyline increases

as the number for dimensions for both algorithms.

However, this increase is more accentuated for the

Pareto dominance skyline. Figure 4 shows that the

size of the fuzzy dominance skyline is larger than

the size provided by the Pareto dominance skyline.

Both algorithms show that the size of the skyline

increases as the number of services increases. This

result is expectable since the fuzzy dominance

would privilege services with compromises between

good and bad values.

6.2 Execution Time and Scalability

Figure 5 and Figure 6 show that the CFFBS is more

scalable than the basic approaches for skyline

Figure 5: Effect of the number of services on the CPU

Time.

Figure 6: Effect of the number of services on the CPU

Time.

computation. This result is significant as the number

of services increases which is due to the pruning

process of the R-Tree structures. Besides,

constructing a consistent fuzzy model allow us to

discard directly dominated points without double-

checking the search space. However, we can notice

that when the number of dimensions increases, the

two algorithms have almost the same performances.

This is because R-Tress structures perform poorly

when the number of dimensions is high.

Table1: Parameters and considered values.

Parameters Values

umber of services 1K, 5K, 10K, 100

umber of dimensions 2d, 3d, 4d, 5





0.1, 0.2

7 CONCLUSIONS

We have addressed in this paper the problem of

QoS-based web service composition. We advanced

that exhaustive search in the context of large-scale

systems is not a practical solution. Hence, Skyline

technique, as it allows reducing the search space can

improve the performance of the composition

methods. We have tackled in this paper the skyline

ICSOFT-PT2015-10thInternationalConferenceonSoftwareParadigmTrends

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with fuzzy preference values to take into

consideration the possible compromises between the

QoS values. So we have proposed a method to

construct from the collected fuzzy values a

consistent fuzzy model that would reduce the time

cost of the double-checking process in the Branch

and Bound Skyline with fuzzy dominance. We have

proved the efficiency and the effectiveness of our

proposed algorithm with an experimental study.

In our future work we will focus on extending

this concept to cover the whole QoS-based

composition process.

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