# Using an Integrated Group Decision Method Based on SVM, TFN-RS-AHP, and TOPSIS-CD for Cloud Service Supplier Selection

Authors: Lian-hui Li; Jiu-cheng Hang; Yang Gao; Chun-yang Mu
Journal: Mathematical Problems in Engineering
 (2017)

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## Abstract

To solve the cloud service supplier selection problem under the background of cloud computing emergence, an integrated group decision method is proposed. The cloud service supplier selection index framework is built from two perspectives of technology and technology management. Support vector machine- (SVM-) based classification model is applied for the preliminary screening to reduce the number of candidate suppliers. A triangular fuzzy number-rough sets-analytic hierarchy process (TFN-RS-AHP) method is designed to calculate supplier’s index value by expert’s wisdom and experience. The index weight is determined by criteria importance through intercriteria correlation (CRITIC). The suppliers are evaluated by the improved TOPSIS replacing Euclidean distance with connection distance (TOPSIS-CD). An electric power enterprise’s case is given to illustrate the correctness and feasibility of the proposed method.


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## Body

## 1. Introduction

Cloud computing [1–4] is a new network application technology, and it is also a great revolution technology after the development of distributed computing, parallel computing, and grid computing. It is a kind of service mode based on shared infrastructure by which software, hardware, platform, and other IT resources will be available to users through the network services.National Institute of Standards and Technology (NIST) has given its definition as follows: cloud computing is a kind of pay-per-use network operation mode which can provide users with available, convenient, on-demand use of network resources [5]. The resources including storage, application software, and computing services go into a configurable resource pool and can be quickly extracted and used. Enterprises do not have to invest a lot of management work; they only need to conduct the necessary interaction with the service providers. Currently, cloud computing is rapidly growing and can be applied in a mature way in many industries. For instance, Amazon, Google, Microsoft, and other IT giants have converted more and more applications into cloud services [1–7]. Cloud services [8] (i.e., cloud computing services) are cloud computing products which are available as a service and provided to users. Users can access the required resources and services in an on-demand and extensible way by the network. By updating to cloud service model, enterprises can effectively reduce the cost of investment, achieve the unified management of resources, sharing, and on-demand use and improve resource utilization. As a result, the market reaction capability and core competitiveness can be enhanced.To develop and implement the cloud service-oriented networked mode for an enterprise or an enterprise union, the most important challenge is how to select the best cloud service supplier under the background of cloud computing emergence [9, 10]. The cloud services measurement initiative consortium (CSMIC) [11] has designed and released the service measurement index framework. Cloud service can be evaluated from seven aspects including accountability, agility, assurance, finance, performance, security privacy, and usability. Building the service medium between cloud service and application need based on this framework has gradually become an important development trend of cloud computing [12, 13].Meanwhile, group decision method based on this framework has become a main method for cloud service supplier selection. Garg et al. proposed a framework for ranking of cloud computing services by analytic hierarchy process (AHP) [14]. Dong and Guo proposed an evaluation and selection approach for cloud manufacturing service based on template and global trust degree [15]. Generally, group decision method in existing researches can be divided into two categories: single methods and combination methods. Single methods mainly include AHP [16], ANP [17], rough sets [18], DEA [19], grey theory [20], fuzzy axiomatic design [21], fuzzy TOPSIS [22], genetic algorithm [23], and COWA operator [24]. Combination methods mainly include threshold method and grey relational analysis [25], AHP and genetic algorithm [26], ANN-MADA [27], ANP-DEA [28], fuzzy DEMATEL-ANP-TOPSIS [29], fuzzy AHP and fuzzy multiobjective linear programming [30], AHP-ISM [31], and AHP-TOPSIS [32].Through the analysis of the existing researches, it can be summarized that cloud service is considered more on the technology perspective but less on the technology management perspective based on the service measurement index framework. Meanwhile, the uncertain preference information processing is lacked. Therefore, we put forward an integrated group decision method for cloud service supplier selection. From two perspectives of technology and technology management, we build the cloud service supplier selection index framework by four criteria: cloud service performance, supplier capability, supplier service level, and supplier service quality. According to the main information of candidate suppliers, support vector machine- (SVM-) based classification model is applied for the preliminary screening to reduce the number of candidate suppliers. Through the investigation and mastery of experts to all suppliers on the indexes, a triangular fuzzy number-rough sets-AHP (TFN-RS-AHP) method is proposed to calculate supplier’s index value by expert’s wisdom and experience. The index weight is determined by criteria importance though intercriteria correlation (CRITIC). Finally, the suppliers are evaluated by improved TOPSIS replacing Euclidean distance with connection distance.


## 2. Index Framework

Cloud service supplier selection index framework is one of the most important problems in the whole evaluation process. CSMIC has given the service measurement index framework. In this framework, cloud service can be evaluated from seven aspects including accountability, agility, assurance, finance, performance, security privacy, and usability. It can be seen that this framework is mainly from the technology perspective.Different suppliers can provide similar or the same cloud service, so cloud service supplier selection is different from cloud service selection. Additionally, cloud service supplier selection has some inherent relevance to the application industry.Considering the characteristics of cloud service supplier from the technology perspective and the technology management perspective, the cloud service supplier selection index framework is built as shown in Figure1 by four criteria (C1: cloud service performance, C2: supplier capability, C3: supplier service level, and C4: supplier service quality) according to systematic, comprehensive, scientific, flexible, and operable principles.Figure 1
The cloud service supplier selection index framework.Cloud service performance criterion, which includes the core content of CSMIC’s service measurement index framework, embodies the technology perspective. Supplier capability criterion, supplier service level criterion, and supplier service quality criterion embody the technology management perspective. Each criterion is further detailed to indexes. The significance of each index is as follows:C11/I1: service resource’s virtualization management, C12/I2: service’s coordination, integration, and intelligence, C13/I3: service mode’s diversity, C14/I4: service’s maintainability, availability, and flexibility, C15/I5: service data’s transmission and storage security, access security, and privacy protection, C16/I6: service’s timeliness, accuracy, reliability, fault tolerance, and robustness, C17/I7: service’s deployment cost, running cost, and maintenance cost, C21/I8: supplier’s operation management and organization management level, C22/I9: supplier’s technical support and training level, C23/I10: supplier’s reputation and implementation experience, C24/I11: supplier’s ability of research development, innovation, and profitability, C31/I12: supplier’s service attitude and sustainability, C32/I13: supplier’s ability to provide value-added and extended services, C33/I14: supplier’s ability of service deployment, running, and maintenance, C41/I15: supplier service’s timely delivery and stability, C42/I16: supplier service’s protocol level and execution ability, and C43/I17: supplier service’s cost-effectiveness.


## 3. Integrated Group Decision Method

### 3.1. Preliminary Screening

Under the linear separable circumstances, the basic idea of SVM [33, 34] can be described as follows. It is assumed that the samples are (x1,y1),…,(xl,yl), x∈Ru, where l is the number of samples and u is the number of input dimensions. A hyperplane is defined as ω·x+f=0 to classify the samples into two types. The classification result is as follows:(1)ω·xi+f≥0,yi=+1ω·xi+f≥0,yi=-1,where ω is the adjustable weight vector and f is the bias amount of the hyperplane. So ω·x represents the scalar product of ω∈Ru and xi∈Ru.The optimal classification hyperplane is shown in Figure2.Figure 2
The optimal separating hyperplane of SVM.To achieve the correct classification of all samples, the classification intervals2/w on both sides should be the largest. Finding the optimal hyperplane can be considered as the quadratic programming problem. For the training sample set, the optimal value of w and b should be found to minimize the cost function; that is,(2)minφw=w22=ωTω2,where the constraint condition is yi(ω·xi+f)-1≥0, i=1,2,…,l.Here the optimization function is quadratic form and the constraint condition is linear, so this is a typical quadratic programming problem which can be solved by Lagrange method. The Lagrange multiplier isξi≥0, i=1,2,…,l, so(3)Γω,f,ξ=12ω2-∑i=1lξiyiω·xi+f-1.The extreme of Γ belongs to saddle point. The minimum ofω and f to Γ can be obtained as ω=ω∗ and f=f∗ while the maximum of ξ to Γ can be obtained as ξ=ξ∗. The optimal hyperplane can be determined by solving quadratic program problem based on the derivative of Γ. As can be seen, only the samples which make ξ=0 can play a role in ω∗ and determine the classification result. These samples are defined as support vectors. Then ω∗ is obtained as follows:(4)ω∗=∑i=1lξi∗yixi.One support vector samplexi:f∗=yi-ω·xi is selected. For any input sample x, the classification function is as follows:(5)dx=ω∗·x+f∗=Γω,f,ξ=∑i=1lyiξi∗xxi+f.The ascription ofx is determined according to the positive or negative sign of d(x). If the samples are linear nonseparable, the linear nonseparable problem can be converted to linear separable problem by nonlinear transformation defined by kernel function.


### 3.2. Index Value Calculating

By rough sets theory [35], the domain U is a nonnull finite set of the objects and Y is an object in U. All objects in U belong to p partitions: S1,S2,…,Sp. These p partitions have an order: S1<S2<⋯<Sp. To any partition Si (1≤i≤p), its upper approximation set is ASUpper(Si)={Y∈K∣K⊆U/R(Y)∧K≥Si} and its lower approximation set is ASLower(Si)={Y∈K∣K⊆U/R(Y)∧K≤Si}, where U/R(Y) indicates the partition of the unclear relationship R in the domain U. Any unclear partition Si in the domain U can be expressed by its rough number. The rough number of Si is composed of the upper bound LUpper(Si)=(∑R(Y))/NUpper(Si), Y∈ASUpper(Si), and the lower bound LLower(Si)=(∑R(Y))/NLower(Si), Y∈ASLower(Si); here NUpper(Si) is the number of objects contained in the upper approximation set of Si and NLower(Si) is the number of objects contained in the lower approximation set of Si. The interval between upper and lower bounds is defined as the rough boundary interval RN(Si)=[LLower(Si),LUpper(Si)]. Therefore, the unclear partition Si in the domain U can be expressed by the rough boundary interval RN(Si)=[LLower(Si),LUpper(Si)] which contains its upper bound and lower bound.The mathematical statistics characteristic of expert scoring method can maximize the values of expert’s wisdom and experience. However, the scores of multiple cloud service suppliers on an index depend on expert’s personal experience and subjective judgment. Expressing the score with a certain number is obviously unreasonable. Compared with certain number, fuzzy number can better reflect the inherent uncertainty of expert scoring. Additionally, the uncertainty can be described as set boundary region by the rough boundary interval. Compared with membership function, set boundary region can better reflect the real judgment of expert and the views of multiple experts can be taken into account. Therefore, a triangular fuzzy number-rough sets-AHP (TFN-RS-AHP) method is proposed to calculate the index value of cloud service supplier.It is assumed that there aren cloud service suppliers after preliminary screening and q experts. To the index It (t=1,2,…,17), the TFN score matrices given by q experts are E1,t,E2,t,…,Eq,t, where Ek,t=(ei,jk,t)n×n (k=1,2,…,q and i,j=1,2,…,n). When i≠j, ei,jk,t=(ai,jk,t,bi,jk,t,ci,jk,t) represents the score of the cloud service supplier j relative to the cloud service supplier i on the index It given by the expert k. When i=j, ei,jk,t=(1,1,1). These matrices E1,t,E2,t,…,Eq,t must pass the consistency inspection. If Ek,t fails, it will be modified by the expert k.Step 1.
E k , t is decomposed into Ak,t=(ai,jk,t)n×n, Bk,t=(bi,jk,t)n×n, and Ck,t=(ci,jk,t)n×n. A1,t,A2,t,…,Aq,t are combined together into a rough group decision matrix At=(Ai,jt)n×n, where Ai,jt={ai,j1,t,ai,j2,t,…,ai,jq,t}.Step 2.
The rough boundary intervals of the scores given byq experts in Ai,jt are RN(ai,j1,t),RN(ai,j2,t),…,RN(ai,jq,t), where RN(ai,jk,t)=[ai,jk-,t,ai,jk+,t], k=1,2,…,q. Then RN(Ai,jt)={[ai,j1-,t,ai,j1+,t],[ai,j2-,t,ai,j2+,t],…,[ai,jq-,t,ai,jq+,t]}. As a result, the average rough interval of Ai,jt is as follows:(6)RNAi,jt=ai,j-,t,ai,j+,t=∑r=1qai,jr-,tq,∑r=1qai,jr+,tq.Step 3.
The rough judgment matrix can be obtained asEAt=(RN(Ai,jt))n×n. EAt can be decomposed into the rough lower boundary matrix EAt- and the rough upper boundary matrix EAt+, where EAt-=(ai,j-,t)n×n and EAt+=(ai,j+,t)n×n. Their characteristic vectors corresponding to the maximum eigenvalue are, respectively, obtained as VAt-=[va1-,t,va2-,t,…,van-,t]T and VAt+=[va1+,t,va2+,t,…,van+,t]T. After averaging, gait=(vai-,t+via+,t)/2, i=1,2,…,n. We can get GAt=ga1t,ga2t,…,gant.Step 4.
Similarly,GBt=gb1t,gb2t,…,gbnt and GCt=gc1t,gc2t,…,gcnt can be obtained. Consequently, the values of n cloud service suppliers on the index It are z1,t,z2,t,…,zn,t, where zi,t=gait,gbit,gcit is a triangular fuzzy number.Step 5.
Using the same method, the value ofn cloud service suppliers on other indexes can be obtained. The triangular fuzzy number index value matrix can be expressed as Z=(zi,t)n×m.Step 6.
The methods of converting triangular fuzzy number into real number mainly are gravity center method and mean square deviation method. To the triangular fuzzy number index valuezi,t=gait,gbit,gcit, its gravity center [36, 37] is c(zi,t)=gait+gbit+gcit/3, and its mean square deviation [36, 37] is (7)σzi,t=gait2+gbit2+gcit2-gait·gbit-gait·gcit-gbit·gcit18.Here, we construct a planning model by introducing the risk preference factor to realize the integration of the two methods. It is assumed that the decision makers tend to use the gravity center method with a risk preference ofξi and tend to use the mean square deviation method with a risk preference of 1-ξi. ξi and 1-ξi are used as the weight of gravity center and mean square deviation, respectively. The triangular fuzzy number zi,t can be described as di,t=(ξi·c(zi,t))2+((1-ξi)·σ(zi,t))2.We construct the planning model:min⁡di,t, s.t. 0≤ξi≤1. The risk preference ξi can be obtained as follows:(8)ξi=czi,t2czi,t2+σzi,t2.As a result, the triangular fuzzy number index value matrix ofn cloud service suppliers can be converted into the real number form D=di,tn×m.The index value matrixD=di,tn×m should be standardized as follows:(9)di,t=di,t-d,t¯vard,t,where d,t¯=1/n∑i=1ndi,t and var(d,t)=1/(n-1)∑i=1n(di,t-d,t¯)2.


### 3.3. Index Weight Determining

Assuming that the vector of index weight isΦ=[ϕ1,ϕ2,…,ϕm]T, weighting methods commonly include entropy method [38], standard deviation method [39], and CRITIC [40].


#### 3.3.1. Entropy Method [38]

According to the entropy theory, the entropy value of the indexIt (t=1,2,…,17) is as follows:(10)EVt=-1ln⁡m∑i=1ndi,td,tln⁡di,td,t,where d,t=∑i=1ndi,t.The larger entropy value means that the values of all cloud service suppliers onIt have a smaller difference. It is generally believed that the index is more important when the values of all suppliers have a larger difference. So the weight of It is as follows:(11)ϕt=1-EVt∑t=1m1-EVt.


#### 3.3.2. Standard Deviation Method [39]

The standard deviation of the indexIt is σt, so the weight of It is as follows:(12)ϕt=σt∑t=1mσt,where σt=1/n∑i=1ndi,t-1/n∑i=1ndi,t2.


#### 3.3.3. CRITIC [40]

The comparison strength with the expression form of standard deviation indicates the value difference of all objects on the same index. The conflict is based on the correlation between two indexes. When the two indexes have a strong positive correlation, the conflict is low. Both comparison strength and conflict should be considered comprehensively.The correlation coefficient [40] of the indexes Ik and Ij is as follows:(13)ccrk,j=∑i=1ndi,k-1/n∑i=1ndi,kdi,j-1/n∑i=1ndi,j∑i=1ndi,k-1/n∑i=1ndi,k2∑i=1ndi,j-1/n∑i=1ndi,j2.The conflict of the indexIj with other indexes can be expressed as follows:(14)conj=∑k=1m1-ccrk,j.Therefore, the weight ofIj is as follows:(15)ϕj=Cj∑j=1mCj,where Cj=σj·conj is the information amount of Ij.Compared with entropy method and standard deviation method, CRITIC, which comprehensively considers the volatility of index value and the conflict between the indexes, can completely reflect the competitive relationship between the indexes. As a result, we choose CRITIC to determine the index weight.


### 3.4. Suppliers Evaluating

The technique for order preference by similarity to an ideal solution (TOPSIS) is a classic multi-index sorting method [41]. Euclidean distances between the object and two ideal points are used to calculate the closeness. The objects on the perpendicular bisector of two ideal points have the same closeness value and cannot be distinguished. Therefore, some improved TOPSIS methods have been proposed such as angle measure evaluation method (TOPSIS-AME) [42] and vertical projection method (TOPSIS-VP) [43]. The former one only considers the angle closeness between the object and two ideal points and ignores the difference in length. When two objects have the same angle closeness but different length, it will draw the wrong conclusion. When two or more objects have the same projective point on the connection line of two ideal points, the latter one also cannot distinguish these objects.The theory of set pair analysis (SPA) [44, 45], proposed by Zhao in 1989, is a systematic analysis method to solve the uncertainty problem with connection degree. A set pair is constructed from two related sets in the uncertainty system; then the sameness, contrariety, and difference analysis will be done on the uncertainty of the set pair; lastly the connection degree of the set pair can be obtained. SPA method can be used to describe the relationship in certainty-uncertainty system.According to the index value matrixD=di,tn×m and the index weight vector Φ=[ϕ1,ϕ2,…,ϕm]T, we can get the weighted index value matrix H=(hi,j)n×m=(ϕj·di,j)n×m.The positive ideal point and the negative ideal point are as follows:(16)H+=h1+,h2+,…,hl+,H-=h1-,h2-,…,hl-,where hi+=max⁡{h1,i,h2,i,…,hn,i} and hi-=min⁡{h1,i,h2,i,…,hn,i}.The weighted index value of the supplierk (k=1,2,…,n) can be expressed as Hk which is the row k of H.The element pairshk1,h1+,hk2,h2+,…,(hkl,hl+) are comprised of the corresponding elements of Hk and H+. Comparing the element pairs hk1,h1+,hk2,h2+,…,(hkl,hl+), there are Nk,+1 pairs in which the difference of hki and hi+ is tiny (i.e., sameness relationship), Nk,+2 pairs in which the difference of hki and hi+ is huge (i.e., contrariety relationship), and Nk,+3 pairs in which the difference of hki and hi+ is existing but not very obvious (i.e., difference relationship) [44, 45]. Nk,+1+Nk,+2+Nk,+3=l. So the connection degree between Hk and H+ can be expressed as D(Hk,H+)=Nk,+1/lΔ+Nk,+2/lΩ+Nk,+3/lΨ, where Δ, Ω, and Ψ are the symbols of the sameness relationship, contrariety relationship, and difference relationship.We assume thatD(Hk,H+)=Θ1·D(hk1,h1+)+Θ2·D(hk2,h2+)+⋯+Θl·D(hkl,hl+), where Dhki,h1+=Aki+·Δ+Bki+·Ω+Cki+·Ψ, i=1,2,…,m. If hki=hi-, Aki+=Cki+=0 and Bki+=1; and if hk,i∈(hi-,hi+), Aki+=hki/hi+, Cki+=1-hki/hi+, and Bki+=0; and if hki=hi+, Aki+=1 and Bki+=Cki+=0. So we can get the connection degree between Hk and H+ as follows:(17)DHk,H+=Ak+Δ+Bk+Ω+Ck+Ψ,where Ak+=∑i=1lAki+/l, Bk+=∑i=1lBki+/l, Ck+=∑i=1lCki+/l.According to SPA theory, the connection vector betweenHk and H+ can be expressed as V(Hk,H+)=(Ak+,Bk+,Ck+)T and the connection vector between H+ and itself is V(H+,H+)=1,0,0T, so the connection distance from Hk to H+ is d(Hk,H+)=(Ak+-1)2+(Bk+)2+(Ck+)2.Similarly, we can get that the connection distance fromHk to H- is d(Hk,H-)=(Ak--1)2+(Bk-)2+(Ck-)2.Lastly, we can get the relative closeness degree fromHk to the ideal points H+ and H-as follows:(18)rck=dHk,H-dHk,H++dHk,H-.The relative closeness degreerck has the following characteristics:(1)
IfHk=H+, rck=1.(2)
IfHk=H-, rck=0.(3)
Whend(Hk,H+)→0 (i.e., Hk≠H+ and Hk≠H-, Hk→H+), rck→1.Therefore, using the connection distance from the object to the ideal points fits well with the basic sorting principles of TOPSIS, so the improved TOPSIS by replacing Euclidean distance with connection distance (TOPSIS-CD) is reasonable. We can calculate the relative closeness from each object to the ideal points successively and obtain the final results by sorting them.


## 3.1. Preliminary Screening

Under the linear separable circumstances, the basic idea of SVM [33, 34] can be described as follows. It is assumed that the samples are (x1,y1),…,(xl,yl), x∈Ru, where l is the number of samples and u is the number of input dimensions. A hyperplane is defined as ω·x+f=0 to classify the samples into two types. The classification result is as follows:(1)ω·xi+f≥0,yi=+1ω·xi+f≥0,yi=-1,where ω is the adjustable weight vector and f is the bias amount of the hyperplane. So ω·x represents the scalar product of ω∈Ru and xi∈Ru.The optimal classification hyperplane is shown in Figure2.Figure 2
The optimal separating hyperplane of SVM.To achieve the correct classification of all samples, the classification intervals2/w on both sides should be the largest. Finding the optimal hyperplane can be considered as the quadratic programming problem. For the training sample set, the optimal value of w and b should be found to minimize the cost function; that is,(2)minφw=w22=ωTω2,where the constraint condition is yi(ω·xi+f)-1≥0, i=1,2,…,l.Here the optimization function is quadratic form and the constraint condition is linear, so this is a typical quadratic programming problem which can be solved by Lagrange method. The Lagrange multiplier isξi≥0, i=1,2,…,l, so(3)Γω,f,ξ=12ω2-∑i=1lξiyiω·xi+f-1.The extreme of Γ belongs to saddle point. The minimum ofω and f to Γ can be obtained as ω=ω∗ and f=f∗ while the maximum of ξ to Γ can be obtained as ξ=ξ∗. The optimal hyperplane can be determined by solving quadratic program problem based on the derivative of Γ. As can be seen, only the samples which make ξ=0 can play a role in ω∗ and determine the classification result. These samples are defined as support vectors. Then ω∗ is obtained as follows:(4)ω∗=∑i=1lξi∗yixi.One support vector samplexi:f∗=yi-ω·xi is selected. For any input sample x, the classification function is as follows:(5)dx=ω∗·x+f∗=Γω,f,ξ=∑i=1lyiξi∗xxi+f.The ascription ofx is determined according to the positive or negative sign of d(x). If the samples are linear nonseparable, the linear nonseparable problem can be converted to linear separable problem by nonlinear transformation defined by kernel function.


## 3.2. Index Value Calculating

By rough sets theory [35], the domain U is a nonnull finite set of the objects and Y is an object in U. All objects in U belong to p partitions: S1,S2,…,Sp. These p partitions have an order: S1<S2<⋯<Sp. To any partition Si (1≤i≤p), its upper approximation set is ASUpper(Si)={Y∈K∣K⊆U/R(Y)∧K≥Si} and its lower approximation set is ASLower(Si)={Y∈K∣K⊆U/R(Y)∧K≤Si}, where U/R(Y) indicates the partition of the unclear relationship R in the domain U. Any unclear partition Si in the domain U can be expressed by its rough number. The rough number of Si is composed of the upper bound LUpper(Si)=(∑R(Y))/NUpper(Si), Y∈ASUpper(Si), and the lower bound LLower(Si)=(∑R(Y))/NLower(Si), Y∈ASLower(Si); here NUpper(Si) is the number of objects contained in the upper approximation set of Si and NLower(Si) is the number of objects contained in the lower approximation set of Si. The interval between upper and lower bounds is defined as the rough boundary interval RN(Si)=[LLower(Si),LUpper(Si)]. Therefore, the unclear partition Si in the domain U can be expressed by the rough boundary interval RN(Si)=[LLower(Si),LUpper(Si)] which contains its upper bound and lower bound.The mathematical statistics characteristic of expert scoring method can maximize the values of expert’s wisdom and experience. However, the scores of multiple cloud service suppliers on an index depend on expert’s personal experience and subjective judgment. Expressing the score with a certain number is obviously unreasonable. Compared with certain number, fuzzy number can better reflect the inherent uncertainty of expert scoring. Additionally, the uncertainty can be described as set boundary region by the rough boundary interval. Compared with membership function, set boundary region can better reflect the real judgment of expert and the views of multiple experts can be taken into account. Therefore, a triangular fuzzy number-rough sets-AHP (TFN-RS-AHP) method is proposed to calculate the index value of cloud service supplier.It is assumed that there aren cloud service suppliers after preliminary screening and q experts. To the index It (t=1,2,…,17), the TFN score matrices given by q experts are E1,t,E2,t,…,Eq,t, where Ek,t=(ei,jk,t)n×n (k=1,2,…,q and i,j=1,2,…,n). When i≠j, ei,jk,t=(ai,jk,t,bi,jk,t,ci,jk,t) represents the score of the cloud service supplier j relative to the cloud service supplier i on the index It given by the expert k. When i=j, ei,jk,t=(1,1,1). These matrices E1,t,E2,t,…,Eq,t must pass the consistency inspection. If Ek,t fails, it will be modified by the expert k.Step 1.
E k , t is decomposed into Ak,t=(ai,jk,t)n×n, Bk,t=(bi,jk,t)n×n, and Ck,t=(ci,jk,t)n×n. A1,t,A2,t,…,Aq,t are combined together into a rough group decision matrix At=(Ai,jt)n×n, where Ai,jt={ai,j1,t,ai,j2,t,…,ai,jq,t}.Step 2.
The rough boundary intervals of the scores given byq experts in Ai,jt are RN(ai,j1,t),RN(ai,j2,t),…,RN(ai,jq,t), where RN(ai,jk,t)=[ai,jk-,t,ai,jk+,t], k=1,2,…,q. Then RN(Ai,jt)={[ai,j1-,t,ai,j1+,t],[ai,j2-,t,ai,j2+,t],…,[ai,jq-,t,ai,jq+,t]}. As a result, the average rough interval of Ai,jt is as follows:(6)RNAi,jt=ai,j-,t,ai,j+,t=∑r=1qai,jr-,tq,∑r=1qai,jr+,tq.Step 3.
The rough judgment matrix can be obtained asEAt=(RN(Ai,jt))n×n. EAt can be decomposed into the rough lower boundary matrix EAt- and the rough upper boundary matrix EAt+, where EAt-=(ai,j-,t)n×n and EAt+=(ai,j+,t)n×n. Their characteristic vectors corresponding to the maximum eigenvalue are, respectively, obtained as VAt-=[va1-,t,va2-,t,…,van-,t]T and VAt+=[va1+,t,va2+,t,…,van+,t]T. After averaging, gait=(vai-,t+via+,t)/2, i=1,2,…,n. We can get GAt=ga1t,ga2t,…,gant.Step 4.
Similarly,GBt=gb1t,gb2t,…,gbnt and GCt=gc1t,gc2t,…,gcnt can be obtained. Consequently, the values of n cloud service suppliers on the index It are z1,t,z2,t,…,zn,t, where zi,t=gait,gbit,gcit is a triangular fuzzy number.Step 5.
Using the same method, the value ofn cloud service suppliers on other indexes can be obtained. The triangular fuzzy number index value matrix can be expressed as Z=(zi,t)n×m.Step 6.
The methods of converting triangular fuzzy number into real number mainly are gravity center method and mean square deviation method. To the triangular fuzzy number index valuezi,t=gait,gbit,gcit, its gravity center [36, 37] is c(zi,t)=gait+gbit+gcit/3, and its mean square deviation [36, 37] is (7)σzi,t=gait2+gbit2+gcit2-gait·gbit-gait·gcit-gbit·gcit18.Here, we construct a planning model by introducing the risk preference factor to realize the integration of the two methods. It is assumed that the decision makers tend to use the gravity center method with a risk preference ofξi and tend to use the mean square deviation method with a risk preference of 1-ξi. ξi and 1-ξi are used as the weight of gravity center and mean square deviation, respectively. The triangular fuzzy number zi,t can be described as di,t=(ξi·c(zi,t))2+((1-ξi)·σ(zi,t))2.We construct the planning model:min⁡di,t, s.t. 0≤ξi≤1. The risk preference ξi can be obtained as follows:(8)ξi=czi,t2czi,t2+σzi,t2.As a result, the triangular fuzzy number index value matrix ofn cloud service suppliers can be converted into the real number form D=di,tn×m.The index value matrixD=di,tn×m should be standardized as follows:(9)di,t=di,t-d,t¯vard,t,where d,t¯=1/n∑i=1ndi,t and var(d,t)=1/(n-1)∑i=1n(di,t-d,t¯)2.


## 3.3. Index Weight Determining

Assuming that the vector of index weight isΦ=[ϕ1,ϕ2,…,ϕm]T, weighting methods commonly include entropy method [38], standard deviation method [39], and CRITIC [40].


### 3.3.1. Entropy Method [38]

According to the entropy theory, the entropy value of the indexIt (t=1,2,…,17) is as follows:(10)EVt=-1ln⁡m∑i=1ndi,td,tln⁡di,td,t,where d,t=∑i=1ndi,t.The larger entropy value means that the values of all cloud service suppliers onIt have a smaller difference. It is generally believed that the index is more important when the values of all suppliers have a larger difference. So the weight of It is as follows:(11)ϕt=1-EVt∑t=1m1-EVt.


### 3.3.2. Standard Deviation Method [39]

The standard deviation of the indexIt is σt, so the weight of It is as follows:(12)ϕt=σt∑t=1mσt,where σt=1/n∑i=1ndi,t-1/n∑i=1ndi,t2.


### 3.3.3. CRITIC [40]

The comparison strength with the expression form of standard deviation indicates the value difference of all objects on the same index. The conflict is based on the correlation between two indexes. When the two indexes have a strong positive correlation, the conflict is low. Both comparison strength and conflict should be considered comprehensively.The correlation coefficient [40] of the indexes Ik and Ij is as follows:(13)ccrk,j=∑i=1ndi,k-1/n∑i=1ndi,kdi,j-1/n∑i=1ndi,j∑i=1ndi,k-1/n∑i=1ndi,k2∑i=1ndi,j-1/n∑i=1ndi,j2.The conflict of the indexIj with other indexes can be expressed as follows:(14)conj=∑k=1m1-ccrk,j.Therefore, the weight ofIj is as follows:(15)ϕj=Cj∑j=1mCj,where Cj=σj·conj is the information amount of Ij.Compared with entropy method and standard deviation method, CRITIC, which comprehensively considers the volatility of index value and the conflict between the indexes, can completely reflect the competitive relationship between the indexes. As a result, we choose CRITIC to determine the index weight.


## 3.3.1. Entropy Method [38]

According to the entropy theory, the entropy value of the indexIt (t=1,2,…,17) is as follows:(10)EVt=-1ln⁡m∑i=1ndi,td,tln⁡di,td,t,where d,t=∑i=1ndi,t.The larger entropy value means that the values of all cloud service suppliers onIt have a smaller difference. It is generally believed that the index is more important when the values of all suppliers have a larger difference. So the weight of It is as follows:(11)ϕt=1-EVt∑t=1m1-EVt.


## 3.3.2. Standard Deviation Method [39]

The standard deviation of the indexIt is σt, so the weight of It is as follows:(12)ϕt=σt∑t=1mσt,where σt=1/n∑i=1ndi,t-1/n∑i=1ndi,t2.


## 3.3.3. CRITIC [40]

The comparison strength with the expression form of standard deviation indicates the value difference of all objects on the same index. The conflict is based on the correlation between two indexes. When the two indexes have a strong positive correlation, the conflict is low. Both comparison strength and conflict should be considered comprehensively.The correlation coefficient [40] of the indexes Ik and Ij is as follows:(13)ccrk,j=∑i=1ndi,k-1/n∑i=1ndi,kdi,j-1/n∑i=1ndi,j∑i=1ndi,k-1/n∑i=1ndi,k2∑i=1ndi,j-1/n∑i=1ndi,j2.The conflict of the indexIj with other indexes can be expressed as follows:(14)conj=∑k=1m1-ccrk,j.Therefore, the weight ofIj is as follows:(15)ϕj=Cj∑j=1mCj,where Cj=σj·conj is the information amount of Ij.Compared with entropy method and standard deviation method, CRITIC, which comprehensively considers the volatility of index value and the conflict between the indexes, can completely reflect the competitive relationship between the indexes. As a result, we choose CRITIC to determine the index weight.


## 3.4. Suppliers Evaluating

The technique for order preference by similarity to an ideal solution (TOPSIS) is a classic multi-index sorting method [41]. Euclidean distances between the object and two ideal points are used to calculate the closeness. The objects on the perpendicular bisector of two ideal points have the same closeness value and cannot be distinguished. Therefore, some improved TOPSIS methods have been proposed such as angle measure evaluation method (TOPSIS-AME) [42] and vertical projection method (TOPSIS-VP) [43]. The former one only considers the angle closeness between the object and two ideal points and ignores the difference in length. When two objects have the same angle closeness but different length, it will draw the wrong conclusion. When two or more objects have the same projective point on the connection line of two ideal points, the latter one also cannot distinguish these objects.The theory of set pair analysis (SPA) [44, 45], proposed by Zhao in 1989, is a systematic analysis method to solve the uncertainty problem with connection degree. A set pair is constructed from two related sets in the uncertainty system; then the sameness, contrariety, and difference analysis will be done on the uncertainty of the set pair; lastly the connection degree of the set pair can be obtained. SPA method can be used to describe the relationship in certainty-uncertainty system.According to the index value matrixD=di,tn×m and the index weight vector Φ=[ϕ1,ϕ2,…,ϕm]T, we can get the weighted index value matrix H=(hi,j)n×m=(ϕj·di,j)n×m.The positive ideal point and the negative ideal point are as follows:(16)H+=h1+,h2+,…,hl+,H-=h1-,h2-,…,hl-,where hi+=max⁡{h1,i,h2,i,…,hn,i} and hi-=min⁡{h1,i,h2,i,…,hn,i}.The weighted index value of the supplierk (k=1,2,…,n) can be expressed as Hk which is the row k of H.The element pairshk1,h1+,hk2,h2+,…,(hkl,hl+) are comprised of the corresponding elements of Hk and H+. Comparing the element pairs hk1,h1+,hk2,h2+,…,(hkl,hl+), there are Nk,+1 pairs in which the difference of hki and hi+ is tiny (i.e., sameness relationship), Nk,+2 pairs in which the difference of hki and hi+ is huge (i.e., contrariety relationship), and Nk,+3 pairs in which the difference of hki and hi+ is existing but not very obvious (i.e., difference relationship) [44, 45]. Nk,+1+Nk,+2+Nk,+3=l. So the connection degree between Hk and H+ can be expressed as D(Hk,H+)=Nk,+1/lΔ+Nk,+2/lΩ+Nk,+3/lΨ, where Δ, Ω, and Ψ are the symbols of the sameness relationship, contrariety relationship, and difference relationship.We assume thatD(Hk,H+)=Θ1·D(hk1,h1+)+Θ2·D(hk2,h2+)+⋯+Θl·D(hkl,hl+), where Dhki,h1+=Aki+·Δ+Bki+·Ω+Cki+·Ψ, i=1,2,…,m. If hki=hi-, Aki+=Cki+=0 and Bki+=1; and if hk,i∈(hi-,hi+), Aki+=hki/hi+, Cki+=1-hki/hi+, and Bki+=0; and if hki=hi+, Aki+=1 and Bki+=Cki+=0. So we can get the connection degree between Hk and H+ as follows:(17)DHk,H+=Ak+Δ+Bk+Ω+Ck+Ψ,where Ak+=∑i=1lAki+/l, Bk+=∑i=1lBki+/l, Ck+=∑i=1lCki+/l.According to SPA theory, the connection vector betweenHk and H+ can be expressed as V(Hk,H+)=(Ak+,Bk+,Ck+)T and the connection vector between H+ and itself is V(H+,H+)=1,0,0T, so the connection distance from Hk to H+ is d(Hk,H+)=(Ak+-1)2+(Bk+)2+(Ck+)2.Similarly, we can get that the connection distance fromHk to H- is d(Hk,H-)=(Ak--1)2+(Bk-)2+(Ck-)2.Lastly, we can get the relative closeness degree fromHk to the ideal points H+ and H-as follows:(18)rck=dHk,H-dHk,H++dHk,H-.The relative closeness degreerck has the following characteristics:(1)
IfHk=H+, rck=1.(2)
IfHk=H-, rck=0.(3)
Whend(Hk,H+)→0 (i.e., Hk≠H+ and Hk≠H-, Hk→H+), rck→1.Therefore, using the connection distance from the object to the ideal points fits well with the basic sorting principles of TOPSIS, so the improved TOPSIS by replacing Euclidean distance with connection distance (TOPSIS-CD) is reasonable. We can calculate the relative closeness from each object to the ideal points successively and obtain the final results by sorting them.


## 4. Case Study

With the rapid development in electric power industry and the continuous improvement of the customers’ requirement for electric safety, the traditional vertical mode is gradually hard to guarantee the whole process of electric power industry under the certain cost and periodic constraints. The service-oriented networked mode, which combines the IT capacity with the traditional electric power industry, provides an effective solution to this problem and realizes the rapid integrating and updating of electric power enterprises. Cloud service platform has greatly facilitated the deep collaboration among different enterprises in the electric power chain. More importantly, the electric power enterprises can gradually shift to service-oriented pattern through the cloud service platform, and the enterprise’s independent innovation and core competitiveness can be continuously improved.To meet the development requirement, the management team of an electric power enterprise has decided to introduce the service-oriented networked mode after careful analysis and discussion.Several important indexes in Figure1 chosen by decision makers are taken as the standard to determine the input vector. According to Formula (2), the classification function can be determined. Due to limited space, the detailed index information is not given. The process of preliminary screening for cloud service supplier selection using SVM classification model is as follows. If dx=ω∗·x+f∗≥0, x will pass. If d(x)=ω∗·x+f∗<0, x will be eliminated. We use SVM toolbox in Matlab to classify twelve qualified suppliers and five suppliers (S1, S2, S3, S4, and S5) pass the preliminary screening.Taking the indexI1 as an example, the TFN score matrices of five suppliers given by three experts are E1,1=(ei,j1,1)5×5, E2,1=(ei,j2,1)5×5, and E3,1=(ei,j3,1)5×5, where ei,j1,1=ai,j1,1,bi,j1,1,ci,j1,1, ei,j2,1=ai,j2,1,bi,j2,1,ci,j2,1, and ei,j3,1=ai,j3,1,bi,j3,1,ci,j3,1. Here,(19)
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.All of them can pass the consistency inspection.We decomposeE1,1 into A1,1, B1,1, and C1,1, decompose E2,1 into A2,1, B2,1, and C2,1, and decompose E3,1 into A3,1, B3,1, and C3,1, respectively.(20)
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.A 1,1, A2,1, and A3,1 are combined together into a rough group decision matrix A1=(Ai,j1)5×5, Ai,j1=ai,j1,1,ai,j2,1,ai,j3,1. (21)
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.Fora1,21,1 = “7/8” in A1,21={7/8,5/6,3}, its upper and lower approximation sets are {7/8,3} and {7/8,5/6}. Its rough boundary interval is RNa1,21,1=[(7/8+5/6)/2,7/8+3/2]=[0.8542,1.9375]. Meanwhile, RNa1,22,1=[0.8333,1.5694] and RNa1,23,1=[1.5694,3]. So the rough boundary interval of A1,21 is RNA1,21=[(0.8542+0.8333+1.5694)/3,(1.9375+1.5694+3)/3]=[1.0856,2.1690]. The rough boundary interval of other elements in A1 can be obtained similarly.The rough judgment matrix can be obtained asEA1=(RN(Ai,j1))5×5. (22)EA1=1,11.0856,2.16900.7407,2.37041.2302,4.58731.2153,3.15280.4284,0.67841,11.1019,3.01850.8505,2.70770.5,0.50.9815,1.79630.6389,2.55561,10.4167,0.76331.2626,4.13130.5057,1.69320.5972,1.75631.0990,2.75281,10.3194,0.59720.9683,4.37730.6667,0.66670.5139,0.90281.7179,2.74361,1.E A 1 can be decomposed into the rough lower boundary matrix EA1- and the rough upper boundary matrix EA1+, where EA1-=(ai,j-,1)5×5 and EA1+=(ai,j+,1)5×5. (23)EA1-=11.08560.74071.23021.21530.428411.10190.85050.50.98150.638910.41671.26260.50570.59721.099010.31940.96830.66670.51391.71791,EA1+=12.16902.37044.58733.15280.678413.01852.70770.51.79632.555610.76334.13131.69321.75632.752810.59724.37730.66670.90282.74361.Their characteristic vectors corresponding to the maximum eigenvalue are obtained asVA1-=-0.5343,-0.3836,-0.4595,-0.3489,-0.4843T and VA1+=-0.5654,-0.3413,-0.4669,-0.3561,-0.4679T.After averaging,GA1=0.5498,0.3624,0.4632,0.3525,0.4761.Similarly,GB1={0.6237,0.3994,0.5608,0.7786,0.5672} and GC1={0.8911,0.4718,0.6601,0.8593,0.7709}. The values of five cloud service suppliers on the index I1 are as follows:(24)z1,1=0.5498,0.6237,0.8911,z2,1=0.3624,0.3994,0.4718,z3,1=0.4632,0.5608,0.6601,z4,1=0.3525,0.7786,0.8593,z5,1=0.4761,0.5672,0.6601.Using the same method, the value of five cloud service suppliers on other sixteen indexes can be obtained. The triangular fuzzy number index value matrixZ=zi,t5×17 is shown in Table 1.Table 1
The triangular fuzzy number index value matrixZ=zi,t5×17 of five cloud service suppliers.
I 1 I 2 I 3 I 4 I 5 I 6 I 7 I 8 I 9 I 1 0 I 11 I 12 I 13 I 14 I 15 I 1 6 I 17 1 (0.5498, 0.6237, 0.8911) (0.1270, 0.6324, 0.8147) (0.0971, 0.6948, 0.9502) (0.6463, 0.6797, 0.7547) (0.1493, 0.8143, 0.8407) (0.2858, 0.5497, 0.8308) (0.3371, 0.4694, 0.7943) (0.8258, 0.9133, 0.9961) (0.1361, 0.1450, 0.5797) (0.5470, 0.6477, 0.6491) (0.2963, 0.4509, 0.7317) (0.3063, 0.5108, 0.4359) (0.2581, 0.4389, 0.5949) (0.4886, 0.8010, 0.9289) (0.0377, 0.3674, 0.9133) (0.0305, 0.1978, 0.7441) (0.5005, 0.7127, 0.9787) 2 (0.3624, 0.3994, 0.4718) (0.0975, 0.9058, 0.9134) (0.1869, 0.4387, 0.7655) (0.5853, 0.7513, 0.9597) (0.1966, 0.6160, 0.9293) (0.0759, 0.5308, 0.9340) (0.5285, 0.6020, 0.6541) (0.4427, 0.7749, 0.9619) (0.0760, 0.5132, 0.6221) (0.1320, 0.3897, 0.4039) (0.1835, 0.1890, 0.6256) (0.3786, 0.5328, 0.7948) (0.1707, 0.1948, 0.4357) (0.2373, 0.5211, 0.9631) (0.7962, 0.8852, 0.9880) (0.4799, 0.5000, 0.9047) (0.0424, 0.0714, 0.6820) 3 (0.4632, 0.5608, 0.6601) (0.5469, 0.9649, 0.9706) (0.2760, 0.4456, 0.7094) (0.2238, 0.2551, 0.3404) (0.3517, 0.5853, 0.9172) (0.0119, 0.1622, 0.5688) (0.1524, 0.2290, 0.5383) (0.3998, 0.8001, 0.8687) (0.1839, 0.4173, 0.9027) (0.0430, 0.2348, 0.8212) (0.4468, 0.4868, 0.5085) (0.5502, 0.5870, 0.9390) (0.1848, 0.9234, 0.9797) (0.2625, 0.3188, 0.5079) (0.1068, 0.1366, 0.7212) (0.6099, 0.6177, 0.8594) (0.0967, 0.5216, 0.8181) 4 (0.3525, 0.7786, 0.8593) (0.1419, 0.4854, 0.9157) (0.0344, 0.3171, 0.8235) (0.5060, 0.5472, 0.8909) (0.2435, 0.2543, 0.2575) (0.1656, 0.2630, 0.3112) (0.0046, 0.0782, 0.1067) (0.1455, 0.5499, 0.8693) (0.3377, 0.3692, 0.4909) (0.3685, 0.6868, 0.7447) (0.6443, 0.8116, 0.8176) (0.2259, 0.2277, 0.8443) (0.1111, 0.2622, 0.4087) (0.0292, 0.5785, 0.7303) (0.4942, 0.6538, 0.7791) (0.1829, 0.2399, 0.8865) (0.1499, 0.7224, 0.8175) 5 (0.4761, 0.5672, 0.6601) (0.6787, 0.7431, 0.8491) (0.3816, 0.4898, 0.7952) (0.1386, 0.6991, 0.9593) (0.2511, 0.3500, 0.4733) (0.0540, 0.1299, 0.7792) (0.0844, 0.2599, 0.8173) (0.3510, 0.4018, 0.8530) (0.0965, 0.2417, 0.7803) (0.0154, 0.1690, 0.3532) (0.3507, 0.6225, 0.8759) (0.3111, 0.4302, 0.9049) (0.0855, 0.2967, 0.4242) (0.2316, 0.4588, 0.5468) (0.7150, 0.8909, 0.9037) (0.0287, 0.1679, 0.4899) (0.4324, 0.4538, 0.8003)By the planning model based on the risk preference, the triangular fuzzy number index value matrixZ=zi,t5×17 is converted into the real number form D=di,t5×17 as shown in Table 2.Table 2
The real number formD=di,t5×17.
I 1 I 2 I 3 I 4 I 5 I 6 I 7 I 8 I 9 I 1 0 I 11 I 12 I 13 I 14 I 15 I 1 6 I 17 1 0.4631 0.2375 0.2816 0.4800 0.3156 0.2852 0.2671 0.8288 0.0646 0.3766 0.2276 0.1709 0.1763 0.5302 0.1421 0.0712 0.5152 2 0.1681 0.3440 0.1895 0.5743 0.2963 0.2119 0.3525 0.5055 0.1385 0.0878 0.0921 0.3092 0.0647 0.2889 0.7887 0.3762 0.0423 3 0.3119 0.6654 0.2124 0.0734 0.3565 0.0413 0.0815 0.4548 0.2120 0.0933 0.2307 0.4640 0.4250 0.1265 0.0731 0.4773 0.1912 4 0.4165 0.2209 0.1119 0.4054 0.0634 0.0590 0.0032 0.2331 0.1573 0.3467 0.5711 0.1513 0.0611 0.1605 0.4059 0.1486 0.2780 5 0.3196 0.5705 0.2938 0.3068 0.1242 0.0663 0.1114 0.2627 0.1045 0.0244 0.3579 0.2708 0.0634 0.1616 0.6961 0.0379 0.3023After the standardization ofD=di,t5×17, the index weight vector determined by CRITIC is Φ = [0.0767, 0.0042, 0.0993, 0.1092, 0.0794, 0.0886, 0.0869, 0.0459, 0.0767, 0.0200, 0.0826, 0.0037, 0.0324, 0.0054, 0.0114, 0.0963, 0.0813]T.According to the standardized index value matrixD=di,t5×17 and the index weight vector Φ, we can get the weighted index value matrix H=hi,t5×17  as shown in Table 3.Table 3
The weighted index value matrixH=hi,t5×17.
I 1 I 2 I 3 I 4 I 5 I 6 I 7 I 8 I 9 I 1 0 I 11 I 12 I 13 I 14 I 15 I 1 6 I 17 1 0.0355 0.0010 0.0280 0.0524 0.0251 0.0253 0.0232 0.0380 0.0050 0.0075 0.0188 0.0006 0.0057 0.0029 0.0016 0.0069 0.0419 2 0.0129 0.0014 0.0188 0.0627 0.0235 0.0188 0.0306 0.0232 0.0106 0.0018 0.0076 0.0011 0.0021 0.0016 0.0090 0.0362 0.0034 3 0.0239 0.0028 0.0211 0.0080 0.0283 0.0037 0.0071 0.0209 0.0163 0.0019 0.0191 0.0017 0.0138 0.0007 0.0008 0.0460 0.0155 4 0.0319 0.0009 0.0111 0.0443 0.0050 0.0052 0.0003 0.0107 0.0121 0.0069 0.0472 0.0006 0.0020 0.0009 0.0046 0.0143 0.0226 5 0.0245 0.0024 0.0292 0.0335 0.0099 0.0059 0.0097 0.0121 0.0080 0.0005 0.0296 0.0010 0.0021 0.0009 0.0079 0.0036 0.0246The positive ideal pointH+ = [0.0355 0.0028 0.0292 0.0627 0.0283 0.0253 0.0306 0.0380 0.0163 0.0163 0.0075 0.0472 0.0017 0.0138 0.0029 0.0090 0.0460 0.0419], and the negative ideal point H- = [0.0129 0.0009 0.0111 0.0080 0.0050 0.0037 0.0003 0.0107 0.0050 0.0050 0.0005 0.0076 0.0006 0.0020 0.0007 0.0008 0.0036 0.0034].The calculation process by TOPSIS-CD is shown in Table4, so the sorting result is S1>S2>S3>S5>S4. The electric power enterprise will select S1 as its cloud service supplier.Table 4
The calculation process by TOPSIS-CD.
The connection distance from the object to the positive ideal point The connection distance from the object to the negative ideal point The connection distance closeness S 1 0.1939 0.1782 0.4789 S 2 0.2912 0.1537 0.3455 S 3 0.3536 0.1224 0.2571 S 4 0.4230 0.1195 0.2203 S 5 0.3051 0.1031 0.2525


## 5. Discussion

The sorting results of the five suppliers by TOPSIS-CD, TOPSIS [41], TOPSIS-AME [42], and TOPSIS-VP [43] are listed in Table 5 and compared in Figure 3. The sorting result by TOPSIS-CD is S1>S2>S3>S5>S4. The sorting result by TOPSIS is S1>S2>S3>S5>S4. The sorting result by TOPSIS-AME is S1>S2>S5>S3>S4. The sorting result by TOPSIS-VP is S1>S2=S3>S5>S4.Table 5
The sorting results of the five suppliers by TOPSIS-CD, TOPSIS [41], TOPSIS-AME [42], and TOPSIS-VP [43].
TOPSIS-CD TOPSIS TOPSIS-AME TOPSIS-VP Closeness Sorting order Closeness Sorting order Closeness Sorting order Closeness Sorting order S 1 0.4789 1 0.5012 1 0.4778 1 0.5032 1 S 2 0.3455 2 0.3988 2 0.4502 2 0.4678 2 S 3 0.2571 3 0.3570 3 0.2445 4 0.4678 2 S 4 0.2203 5 0.1987 5 0.1890 5 0.3089 5 S 5 0.2525 4 0.2456 4 0.3980 3 0.4345 4Figure 3
The comparison of the sorting results of the five suppliers by TOPSIS-CD, TOPSIS [41], TOPSIS-AME [42], and TOPSIS-VP [43].Overall trends of the sorting results by the four methods are generally consistent. The best supplier isS1 and the worst supplier is S4. The sorting result of TOPSIS-CD is the same as the result of TOPSIS, so the validity of TOPSIS-CD can be demonstrated. For the obvious insufficiency proved by many scholars, TOPSIS is not desirable.By TOPSIS-AME, the sorting result of the suppliersS3 and S5 is S3<S5 which is obviously opposite to the sorting result by the other three methods. By TOPSIS-VP, the suppliers S2 and S3 have the equal closeness to ideal points and cannot be sorted. These two methods cannot meet the sorting requirement in some special cases which is consistent with the above analysis in Section 3.4.Based on the above discussion, the proposed integrated group decision method for cloud service supplier selection mainly has the advantages as follows:(1)
SVM-based classification model is applied for the preliminary screening. The number of candidate suppliers is reduced which can decrease the computation of following algorithm.(2)
TFN-RS-AHP method is designed to calculate supplier’s index value which not only can make the most of expert’s wisdom and experience but also can reflect the uncertainty of expert judgment.(3)
TOPSIS-CD is put forward to sort the cloud service suppliers by their weighted index value which is better than TOPSIS, TOPSIS-AME, and TOPSIS-VP.


## 6. Conclusion

With the combination with the new cloud computing technology, many industries are rapidly promoting their information revolution, and the new development mode has emerged now. An important challenge, which enterprise must face, is how to select the best cloud service supplier.In this paper, the cloud service supplier selection index framework is built from two perspectives of technology and technology management. An integrated group decision method is proposed based on SVM, TFN-RS-AHP, and TOPSIS-CD for cloud service supplier selection. However, a large number of mathematical calculations may exist in the proposed method, and the method may be very cumbersome and complex in the practical application. The subjective preference of expert is still difficult to be represented. In the future, we will focus on the expression and quantification of the preference of expert and the extension and application of the proposed method in other fields.



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*Source: 3143502-2017-01-31.xml*