CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

The Assessment of Cloud Computing Service under 
Intuitionistic Fuzzy Environment 

Jingyi Bo*, Yubin Wang, Min Liu 

College of Math and Information Science & Technology, Hebei Normal University of Science& Technology 
Qinhuangdao, Hebei, 066004, China, 
qhdbjy@126.com 
                               
With the rapid development of advanced technology, cloud computing technology has appeared and attracted 
much attention in academia and the business community. In cloud computing technology, cloud computing 
service is a very important issue. Up to now, although cloud computing service achieved some success with 
the development to the deepening of the application, owing to security, technology, management, and other 
constraints, not all businesses are suitable for the use of this service model, so the business need consider 
their own actual situation and select a method to make effective evaluation of the comprehensive capacity of 
the cloud computing services. Thus, according to these characteristics, in this paper, we analysis cloud 
computing service from security and risk, data, services, resources, economic dimensions and then introduce 
a new multiple attribute decision making method to assess cloud computing service where a cloud computing 
service adaptability evaluation system is constructed. Finally, the proposed method is applied in an illustrative 
example to demonstrate its applicability and validity. 

1. Introduction  

Since cloud computing appeared, it has attracted a huge amount of attention from academia and the business 
community. Some researchers insist that cloud computing has emerged as a paradigm to deliver on demand 
resources such as infrastructure, platform, software and so on to customers similar to other utilities as water, 
electricity and gas (Garg et al. 2013; Karthic et al. 2012). In general, there are three main services provided by 
cloud computing architecture based on the needs of IT customers including software, platform and 
infrastructure (He. 2012). The aim of cloud computing is to deliver a network of virtual services so that users 
can access them from anywhere in the world on subscription at competitive costs depending on their quality 
service requirements (Zheng et al. 2013). In general, cloud computing services can offer significant benefits to 
businesses and communities by freeing them from the low-level task of setting up IT infrastructure (Sobel et al. 
2008). Because of business benefits provided by cloud computing, many organizations have started to 
construct applications on the cloud infrastructure and elastic cloud services (Zhang et al. 2012). Each cloud 
provider offers similar cloud services as different prices and performance levels with different sets of features 
(Iosup et al. 2011). Thus, given the diversity of cloud service offerings, a critical problem for customers is to 
discover cloud computing service which is the appropriate one that satisfies the requirements of the 
organizations. However, up to now, although cloud computing service achieved some success with the 
development to the deepening of the application, owing to security, technology, management, and other 
constraints, not all businesses are suitable for the use of this service model, so the business need consider 
their own actual situation and select a method to make effective evaluation of the comprehensive capacity of 
the cloud computing services. 
Thus, how to select an optimal cloud computing service is a big challenge in the study of cloud computing. 
Many researchers devoted to develop methods to deal with this challenge. Techniques including the analytic 
hierarchy process, analytic network process (Buyukazici and Sucu. 2003), outranking (Xu and Shen, 2014), 
VIKOR, TOPSIS and so on are introduced to solve this problem. Hereinto, multiple attribute decision making 
method (Chen. 2014; Zeleny. 1982) is a popular way to handle this problem. Multiple attribute decision making 
method which address decision situations where a decision maker express preferences on multiple attribute 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651103

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Bo J.Y., Wang Y.B., Liu M., 2016, The assessment of cloud computing service under intuitionistic fuzzy 
environment, Chemical Engineering Transactions, 51, 613-618  DOI:10.3303/CET1651103   

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and attempt to find a common solution has been widely discussed in recent years. Generally, the decision 
maker expresses their judgments depending on both the nature of the features describing the alternatives and 
on their own knowledge and experience. But there is also a challenge about how to obtain the preference of 
the decision maker exactly and objectively. Many attempts have been done such as interval-value, fuzzy 
numbers, intuitionistic fuzzy numbers (Atanassov. 1986), hesitant fuzzy numbers and dual hesitant fuzzy 
numbers. Because of the characteristics of intuitionistic fuzzy numbers (Atanassov. 1994), this paper 
introduced intuitionistic fuzzy numbers to express the preference of the decision maker related to several 
alternatives on several attributes. 
In this paper, based on the framework of multiple attribute decision making, we analyze cloud computing 
service from security and risk, data, services, resources, economic dimensions. Then based on t-conorm an t-
norm we define an intuitionisitc fuzzy Hamacher operator to aggregate the intuitionistic fuzzy assessments of 
each alternative on all attributes. Then, using score function and accuracy function, the comprehensive 
assessment of each cloud computing service will be calculated. Based on the mentioned work, the optimal 
alternative can be generated. 
The rest of this pape is demonstrated in the following. Section 2 describes the basic concepts of intuitionistic 
fuzzy sets and their operational laws. In addition, a cloud computing service adaptability evaluation system is 
constructed as the base of this paper. Section 3 demonstrates the proposed multiple attribute decision making 
method and its procedure. Section 4 shows the appliction of the proposed method to verify the applicability of 
the proposed method. Stection 5 concludes this paper. Section 6 gives the references in this paper. 

2. Preliminary  

In this section, the concept of intuitionistic fuzzy set is introduced and corresponding operational laws are 
demonstrated. Then, assessment systems of cloud computing service is constructed in order to the implement 
of the proposed method in section 3. 

2.1 Intuitionistic fuzzy sets 

In this section, some concepts of intuitionistic fuzzy sets are introduced to deal with multiple criteria decision 
making problem.  
Definition 1. Let X be a universe of discourse, then a fuzzy set is defined as: 

A={[x,uA(x)]xX}   (1) 

which is characterized by a membership function uA:X[0,1], where uA denotes the degree of membership of 
the element x to the set A. 
Definition 2. Let X be an ordinary finite non-empty set. An intuitionisitc fuzzy set (Atanassov. 1986) in X is an 
expression A given by 

A={[x,uA(x), vA(x)]xX}   (2) 

where uA:X[0,1] denotes the degree of membership and vA:X[0,1] denotes the degree of non-membership 
with the condition: 0uA+vA1, for all elements x in the set X.  
For each intuitionistic fuzzy set A in X, if the amount  

( ) 1 ( ) ( ),
A A A

x u x v x x X      .  

For computational convenience, in this paper, (uA(x), vA(x)) is called as an intuitionistic fuzzy number. 
Definition 3. Let a=(ua, va) and b=(ub, vb) be two intuitionistic fuzzy numbers, then it can be obtained that 

(1) ( , )
a b a b a b

a b u u u u v v    ;  

(2) ( , )
a b a b a b

a b u u v v v v    ; 

(3) (1 (1 ) , ( ) ), 0
a a

a u v
 

     ;  

(4) (( ) ,1 (1 ) ), 0
a a

a u v
  

    . 

Definition 4. Given two intuitionistic fuzzy values A and B, the following operations are valid: 

(1) a b b a   ;  

(2)  1 1 1a b a b     ;  

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(3) 
1 2 1 2

( )a a a      . 

Definition 5. Let a = (u, v) be an intuitionsitic fuzzy number, a score function S of an intuitionistic fuzzy number 
can be represented in the following. 

S ( a ) = u - v ,  S ( a )  [ - 1 , 1 ]                                                             ( 3 ) 

Definition 6. Let a = (u, v) be an intuitionsitic fuzzy number, an accuracy function H of an intuitionistic fuzzy 
number can be represented in the following. 

H(a)=u+v, H(a)[0,1]                                                                                    (4) 

According to the score function S and the accuracy function H, an order relation between two intuitionistic 
fuzzy numbers is defined as below. 
Definition 7. Let a1 = (u1, v1) and a2 = (u2, v2) be two intuitionistic fuzzy numbers, S(a1) = u1 - v1 and S(a2) = u2 - 
v2 be the scores of a1 and a2, respectively, and let H(a1) = u1 + v1 and H(a2) = u2 + v2 be the accuracy degrees 
of a1 and a2, respectively, then we can acquire the following characteristics: 
(1) if S(a) < S(b), then a is smaller than b, denoted by a< b; 
(2) if S(a) < S(b), then we can obtain that 
if H(a) < H(b), then a is smaller than b, denoted by a< b; 
if H(a) < Hb), then a is equal to b, denoted by a = b. 

2.2 Assessment system of cloud computing service  

Based on the analyses in Introduction, cloud technology connects a network of virtualized computers that are 
dynamically provisioned as computing resources. Cloud computing is a model for enabling ubiquitous, 
convenient, on-demand network access to a shared pool of configurable computing resources that can be 
rapidly provisioned and released with minimal management effort or service provider iteration. Although the 
development of cloud computing is still in the primary stage and relevant technology and schema are not 
mature, due to the advantages of cloud computing service, many companies are interested in cloud computing 
service. Then, how to help the company which is the user to select appropriate and adaptive cloud computing 
service is an important problem. In order to deal with this problem, the first step is to construct a cloud 
computing service adaptability evaluation system in Figure 1. 
 

security and risk data services resources economy

cloud computing service  evaluation system

 

Figure 1: The attributes of cloud computing service evaluation system 

In general, how to construct a scientific and rational evaluation system is a difficult task. There are some 
criteria that should be complied including objectivity, operability, systematic, the combination of qualitative and 
quantitative and so on. The mentioned five attributes including security and risk, data, services, resources, 
economy are also based on these criteria. These five attributes are the second level of evaluation system. 
They can be divided into many other sub-attributes in the third or fourth level. However, the purpose of this 
paper is to assess cloud computing service from the view of global level. Thus, the first level of attributes is 
enough to achieve this goal. Then, in the next section, we will introduce the proposed method and the 
procedure of the method in detail. 

3. Multiple attribute decision making method 

In this section, in order to evaluate the performance of cloud computing service evaluation system, we 
propose a new multiple attribute decision making method with intuitionistic fuzzy information. 

3.1 Construction of the basic model 

For an evaluation problem, the first step is to construct the decision matrix D=[aij]mn, where all the arguments 

615



aij(i=1,2,…m; j=1,2,…n) are intuitionistic fuzzy numbers provided by the decision maker. As for every 
alternative ai(i=1,2,…m), the decision maker is invited to express assessment or preference based on each 
attribute cj(j=1,2,…n) by a intuitionistic fuzzy number aij=(uij, vij)(i=1,2,…m; j=1,2,…n), where uij indicates the 
hesitant degree that the decision maker considers what the alternative ai should satisfy the attribute cj, vij 
indicates the hesitant degree that expert e considers what the alternative ai should not satisfy the attribute 
cj.Then according to the mentioned above, a decision making matrix can be obtained in the following: 

11 12 1

21 22 2

1

n

n

m mn

a a a

a a a
D

a a

 
 
 
 
 
 

 

3.2 Hamacher t-conorm and t-norm 

T-norm and t-conorm are widely applied in fuzzy context to define generalized intersection and union 
operations of fuzzy set. 
Definition 8. Given a function T:[0,1][0,1][0,1], it is called a t-norm when it satisfies the following four 
constraints: 
(1) T(1, x) = x, for all x; 
(2) T(x, y) = T(y, x), for all x and y; 
(3) T(x, T(y, z)) = T(T(x, y), z), for all x, y, and z; and  
(4) If x ≤ x1 and y ≤ y1, then T(x, y) ≤ T(x1, y1). 
Definition 9. Given a function S:[0,1][0,1][0,1], it is called a t-conorm when it satisfies the following four 
constraints: 
(1) S(0, x) = x, for all x; 
(2) S(x, y) = S(y, x), for all x and y; 
(3) S(x, S(y, z)) = S(S(x, y), z), for all x, y, and z; 
(4) If x ≤ x1 and y ≤ y1, then S(x, y) ≤ S(x1, y1). 
A strict Archimedean t-norm T(x, y) = p-1(p(x) + p(y)) can be created from a strictly decreasing function 

: [0,1] [0, ]p    such that p(1) = 0, whose dual function q(x) = p(1-x) can be used to construct a strict 
Archimedean t-conorm S(x, y) = q-1(q(x) + q(y)). 
Given a specific p(x), i.e., 

p(x) = 
(1 )

log
r r x

x

  
 
 

, r > 0,                                                                                             (5) 

It is clear that  

q(x) = p(1-x) = 
(1 ) (1 )

log
1

r r x

x

    
 

 
.                                                                                       (6) 

Under this condition, strict Archimedean t-norm and t-conorm are called Hamacher t-norm Tr(x, y) and t-
conorm Sr(x, y), which are calculated by 

( , )
( 1) ( )

r

xy
T x y

r r x y xy


    
 and                                                                                 (7) 

( 2)
( , )

1 ( 1)
r

x y r xy
S x y

r xy

  


 
, r >0.                                                                                                             (8) 

Tr(x, y) and Sr(x, y) are also called Hamacher product   and Hamacher sum  . Specifically, Tr(x, y) and 
Sr(x, y) reduce to algebraic t-norm and t-conorm when r = 1; while they become Einstein t-norm and t-conorm 
when r = 2 (Liu. 2014). 
Then, based on the mentioned analysis, we can obtain the Hamacher arithmetic weighted averaging operator 
of intuitionistic fuzzy numbers as below: 

IFHWA(a1, a2,. . ., an) =  = 1 1iw a  2 2iw a  …  n inw a  =  

( 1
1

( ( ))
n

j ijj
q w q a


 ,
1

1
( ( ))

n

j ijj
p w p a


 ) =  

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( 1 1

)

1 1

(1 ( 1) ) (1 )

(1 ( 1) ) ( 1) (1 )

j j

j j

n n
w w

ij ij

j j

n n
w w

ij ij

j j

r a a

r a r a

 

 

   

    

 

 
, 1

1 1

( )

(1 ( 1)(1 )) ( 1) ( )

j

j j

n
w

ij

j

n n
w w

ij ij

j j

r a

r a r a



 

    



 
).                            (9) 

3.3 The process of the multiple attribute decision making method 

In this section, the process of the proposed method is demonstrated as below in order to help the decision 
maker obtain the optimal decision. 
Step 1. The decision makers give their assessments of alternative ai(i=1,2,…m) with respect to attribute 
ci(i=1,2,…n), which are expressed by intuitionistic fuzzy numbers aij(i=1,2,…m; j=1,2,…n). In addition, the 
intuitionistic fuzzy decision making matrix should be transformed into normalized matrix. 
Step 2. The decision maker specifies the subject weights of attributes according to his knowledge, experience 
and provided information. 
Step 3. For alternative ai, all the intuitionistic fuzzy numbers should be aggregated into a global value by 
means of the intuitionistic fuzzy Hamacher weighted average (IFHWA) operator. 
Step 4. Then, the scores and accuracy of the global intuitionistic fuzzy number can be calculated in 
accordance with Definition 7. 
Step 5. Rank all the alternatives ai(i=1,2,…m) and select the optimal alternative according to the scores and 
accuracy. 
Step 6. End. 

4. Illustrative example  

In this section, the proposed multiple attribute decision making method is applied in a real case to verify 
applicability and availability of the proposed method. 
Firstly, the decision maker is invited to select an optimal cloud computing service of a company from 
alternatives A1, A2, A3 and A4 on the attributes C1, C2, C3, C4 and C5 including security and risk, data, services, 
resources, economy illustrated in Figure 1. Then, the decision maker gives the assessments of each 
alternative on each attribute in Table 1. 

Table 1:  Original intuitionistic fuzzy decision matrix 

 C1 C2 C3 C4 C5 

A1 (0.2,0.6) (0.5,0.5) (0.8,0.1) (0.4,0.6) (0.6,0.3) 

A2 (0.4,0.5) (0.6,0.3) (0.4,0.4) (0.5,0.3) (0.7,0.1) 
A3 (0.8,0.2) (0.7,0.2) (0.9,0.1) (0.5,0.4) (0.3,0.6) 
A4 (0.7,0.2) (0.5,0.4) (0.3,0.5) (0.1,0.7) (0.4,0.6) 

Then, after obtaining the decision matrix, the decision maker specifies the subject weights of attributes 
denoted as wi = {0.15, 0.2, 0.35, 0.2, 0.1}. Based on the Step 4 and Step 5 in Section 3.3, the decision result 
of this selection problem is acquired in Table 2. Here, the proposed operator and score or accuracy function 
are applied. So, the alternative A4 should be selected as the optimal cloud computing service in the company. 
In this process, the proposed method is very useful for company to make this decision and can be extended 
into group decision making in the future. 

Table 2: Ranking order of all alternatives 

 rank 

A1 2 

A2 3 
A3 1 
A4 4 

5. Conclusion 

Clouds are next-generation data-storage and computing systems with virtualization as the core, enabling 
technology to interconnect and manage distributed computers where resources and dynamically provisioned 

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on demand as a personalized inventory to meets a specific service level agreement. Now, although cloud 
computing service achieved some success with the development to the deepening of the application, owing to 
security, technology, management, and other constraints, not all businesses are suitable for the use of this 
service model, so the business need consider their own actual situation and select a method to make effective 
evaluation of the comprehensive capacity of the cloud computing services. Thus, in this paper, cloud 
computing service is analyzed from security and risk, data, services, resources, economic dimensions and 
then introduce a new multiple attribute decision making method to assess cloud computing service where a 
cloud computing service adaptability evaluation system is constructed. Finally, the proposed method is applied 
in an illustrative example to demonstrate its applicability and validity. 

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