Computers, Materials & Continua
DOI:10.32604/cmc.2022.024676
images

Article

An Integrated Framework for Cloud Service Selection Based on BOM and TOPSIS

Ahmed M. Mostafa*

Computer and Systems Engineering Department, Faculty of Engineering at Helwan, Helwan University, Cairo, 11795, Egypt
*Corresponding Author: Ahmed M. Mostafa. Email: AHMED_YOUSSEF01@h-eng.helwan.edu.eg
Received: 27 October 2021; Accepted: 12 January 2022

Abstract: Many businesses have experienced difficulties in selecting a cloud service provider (CSP) due to the rapid advancement of cloud computing services and the proliferation of CSPs. Many independent criteria should be considered when evaluating the services provided by different CSPs. It is a case of multi-criteria decision-making (MCDM). This paper presents an integrated MCDM cloud service selection framework for determining the most appropriate service provider based on the best only method (BOM) and technique for order of preference by similarity to ideal solution (TOPSIS). To obtain the weights of criteria and the relative importance of CSPs based on each criterion, BOM performs pairwise comparisons of criteria and also for alternatives on each criterion, and TOPSIS uses these weights to rank cloud alternatives. An evaluation and validation of the proposed framework have been carried out through a use-case model to prove its efficiency and accuracy. Moreover, the developed framework was compared with the analytical hierarchical process (AHP), a popular MCDM approach, based on two perspectives: efficiency and consistency. According to the research results, the proposed framework only requires 25% of the comparisons needed for the AHP approach. Furthermore, the proposed framework has a CR of 0%, whereas AHP has 38%. Thus, the proposed framework performs better than AHP when it comes to computation complexity and consistency, implying that it is more efficient and trustworthy.

Keywords: Cloud computing (CC); multiple-criteria decision-making (MCDM); cloud service providers (CSPs); analytical hierarchical process (AHP); the best only method (BOM); technique for order of preference by similarity to ideal solution (TOPSIS)

1  Introduction

Cloud computing [1] is critical for start-ups and small businesses that want to launch a low-cost business model. The concept describes a novel utility computing type for providing customers with storage, computing resources, platforms, software, etc., on a pay-per-use basis through the Internet [2]. Its primary goal is to deliver services ranging from computing resources to applications through the Internet that is accessible at any time and from any location. The advantages of cloud hosting, such as scalability, flexibility, and dependability, have driven businesses to rely on it for their enterprises, resulting in an exponential increase in cloud customers [3]. Cloud computing consists of three parts: (i) cloud service providers (CSPs), (ii) data owners, and (iii) users. CSP acts as the central authority in a cloud environment by controlling all operations. The cloud server holds data stored by data owners, while users can access this data and services [4,5]. Numerous CSPs have made it challenging for customers to the most appropriate CSP that meets their functional and non-functional needs [6]. CSPs should be assessed against a set of quality-of-service (QoS) metrics, along with a method for ranking them based on those metrics to select the best provider [7]. Consequently, the world’s largest organizations have formed the cloud services measurement initiative consortium (CSMIC) [8], which aims to standardize the QoS metrics used to evaluate the quality of service offered by CSPs. The CSMIC developed a model known as the service measurement index (SMI), which includes seven primary criteria such as usability and security. Each criterion was subdivided into several sub-criteria. Cloud customers use these criteria to evaluate different CSPs. Thus, choosing a cloud service provider requires multiple-criteria decision-making (MCDM). The goal of MCDM is to evaluate and rank alternatives (CSPs) based on the selected criteria [9]. Cloud customers will find it incredibly challenging to select the most appropriate CSP based on their preferences due to many existing CSPs and the wide range of evaluating criteria. The selection of cloud services has been the subject of several recent studies [10–12]. Even though these studies have been validated thoroughly, they still have flaws, including low comparison consistency and increased processing complexity, which remain major issues in the selection of cloud services. A consistent, robust, and computationally efficient MCDM framework is presented in this paper. In order to rank the available CSPs, the proposed framework combines the TOPSIS technique and our developed BOM method. The BOM is used to determine the relative weights of alternatives and the weights of criteria. These weights are used by TOPSIS to rank cloud alternatives. Fig. 1 shows the structure of the proposed integrated framework and its interaction with cloud customers and decision-makers.

The proposed integrated framework was validated using a use-case model, demonstrating its efficiency and consistency. In addition, it was compared with the AHP method. Results clearly demonstrate that the proposed framework is robust, efficient, and entirely consistent compared to the AHP method.

The rest of the paper is organized as follows: AHP and TOPSIS methods are discussed in Section 2, and related work is presented in Section 3. A detailed description of the proposed integrated framework is provided in Section 4. In Section 5, experimental results using a use-case model are presented. Section 6 provides an evaluation of our proposed framework and compares it to AHP. Section 7 concludes the paper.

Figure 1: The proposed framework

2  Background

2.1 AHP

For solving complex decisions, Saaty’s AHP is one of the most commonly used methods [13–15]. Specifically, it identifies the goals, the criteria, the subcriteria, and the alternatives for solving a problem. In choosing the best alternative, the AHP allows both objective and subjective factors to be considered, mainly when the subjective preferences of decision-makers play a significant role [16,17]. Three components underlie the AHP method: decomposition, comparative judgments, and prioritization. Based on the principle of decomposition, a problem may be viewed as a hierarchical system. The first level represents the overall objective, while the subsequent levels represent the criteria and alternatives. A comparative judgment is made by comparing elements at each level relative to one element at the next upper level, beginning at the first level of the hierarchy and proceeding downward. A set of preference matrices are produced due to comparing elements at each level [18]. Saaty’s scale of relative preference provides the decision-maker with the basis for their judgments [19].

Let us suppose that we have n criteria c1,c2,⋯,cn. Matrix “A” represents the relative preference of the criteria based on n×n pairwise comparisons as in Eq. (1).

A=(a11a12a21a22⋯a1n⋯a2n⋮⋮an1an2⋱⋮⋯ann)(1)

aij indicates the relative preference (importance) of criterion ai over aj, and i,j=1,2,3,…,n.

where:

aij=1, indicates that criteria i and j are equally important.

aij>1, indicates that the importance of criterion i is more significant than criterion j.

aij<1, indicates that the importance of criterion i is less than criterion j.

The decision-maker is presumed to be consistent in his/her judgments concerning any pair of alternatives. Furthermore, when compared with themselves, all alternatives are ranked equally. Thus, we have aij=1/aji (the property of reciprocal) and aii=1 [17]. Thus, matrix “A” may only need n×(n−1)/2 comparisons.

As demonstrated in [13], if matrix “A” is perfectly consistent, Eq. (1) can be rewritten as follows:

A=(w1w1w1w2w2w1w2w2⋯w1wn⋯w2wn⋮⋮wnw1wnw2⋱⋮⋯wnwn)(2)

where w1,w2,⋯,wn represent the corresponding weight of each criterion c1,c2,⋯,cn, respectively. Each criterion’s weight value may be calculated using Eq. (3) as follows:

(a11a12a21a22⋯a1n⋯a2n⋮⋮an1an2⋱⋮⋯ann)(w1w2⋮wn)=n(w1w2⋮wn)(3)

Accordingly, n is referred to as the principal eigenvalue of matrix “A”, and its eigenvector is w=(w1w2⋯wn)T [13].

When making real-world decisions, we are unable to specify the precise values of wi/wj; only estimated values may be stated. It is essential to consider the possible errors of judgment that a decision-maker might make when providing estimates of these values. The theory of eigenvalue states that a relatively minor alteration in a simple eigenvalue will lead to an eigenvalue issue as follows [13]:

Aw=λmaxw(4)

w1+w2+⋯+wn=1(5)

Here, matrix “A” is inconsistent although still reciprocal, and its principal eigenvalue is λmax.

The weight values of the criteria may now be determined by solving Eqs. (4) and (5). After calculating the overall score value for each alternative, the next step is to determine the ranking of these alternatives according to this score. Based on the following formula on (6), final alternative scores were obtained:

Ri=∑j=1nwjVij(6)

where Ri represents the weight of alternative i, wj represents the weight of criterion j, Vij represents the weight of alternative i relative to criterion j , and n is the number of criteria.

The consistency index (CI) is calculated as the negative average of the other roots of the characteristic polynomial of matrix “A” using the following formula [13]:

CI=λmax−nn−1(7)

A random index (RI) is similar to CI, except it is calculated as an average over many matrices of the same order that are reciprocal and constructed with random entries. The RI values corresponding to each value of n are given in Tab. 1 [20].

According to the AHP method, consistency ratio (CR), a measure of the reliability of an MCDM method’s output, can be computed as follows:

CR=CIRI(8)

According to [13], if the consistency ratio of matrix “A” is less than or equal to 10%, the estimate is considered valid. Otherwise, consistency should be improved. If CR = 0, then values in matrix “A” are entirely consistent, and the following property is met for all of its elements [21]:

aik×akj=aij∀i,k,j(9)

Compared with other multi-criteria approaches, AHP provides flexibility, simplicity, and the capability to detect inconsistencies. However, the disadvantage of AHP is that it requires a substantial number of pairwise comparisons equal to (n(n−1)/2), which dramatically leads to complex computation [22]. Furthermore, there will likely be inconsistencies in pairwise comparisons, which often occur in practice [23].

2.2 TOPSIS

TOPSIS [24] is commonly regarded as one of the popular techniques used to solve MCDM problems. A basic idea of TOPSIS is that the optimal solution should be at the shortest Euclidian distance from the ideal positive solution. At the same time, it needs to be at the longest Euclidian distance from the ideal negative solution [25]. Accordingly, the best alternative is determined based on the Euclidian distance between each alternative and the ideal and the worst alternatives. The TOPSIS steps are outlined below.

Step 1: Construct the decision matrix “D” of size m×n where m and n are the numbers of alternatives and criteria, respectively. It is represented in Eq. (10).

D=(d11d12d21d22⋯d1n⋯d2n⋮⋮dm1dm2⋱⋮⋯dmn)(10)

where dij is the weight of alternative i relative to criterion j.

Step 2: As each criterion is of a different type and thus has a different scale, calculate the normalized decision matrix “K” using Eq. (11) as shown below.

kij=dij∑i=1mdij2,i=1,2,3,…,mandj=1,2,3,…,n.(11)

where kij is the normalized weight of alternative i relative to criterion j.

Step 3: Calculate the weighted matrix “H” based on Eq. (12) by multiplying the wjvalues of the criteria by the corresponding normalized decision matrix elements kij.

hij=wj∗kij(12)

where i=1,2,3,…,m and j=1,2,3,…,n.

Step 4: Utilize the following equations to determine the positive ideal solution (PIS) and the negative ideal solution (NIS):

for beneficial criterion:

xj+=max(h1j,h2j,….,hmj)(13)

xj−=min(h1j,h2j,….,hmj)(14)

and for non-beneficial criterion:

xj+=min(h1j,h2j,….,hmj)(15)

xj−=max(h1j,h2j,….,hmj)(16)

Then:

PIS={x1+,x2+,…,xn+}(17)

NIS={x1−,x2−,…,xn−}(18)

Step 5: For each alternative, calculate the Euclidian distance Ei+ and Ei− using Eqs. (19)–(20).

Ei+=∑j=1n(hij−xj+)2(19)

Ei−=∑j=1n(hij−xj−)2(20)

Step 6: Calculate the closeness value for each alternative (CVi) using Eq. (21):

CVi=Ei−Ei−+Ei+(21)

Step 7: Rank the alternatives according to the closeness value. The best alternative is the one with the highest closeness value, which will be the first in the ranked list.

3  Related Work

A significant challenge associated with cloud computing has been selecting cloud services due to the large number of providers who offer similar services. For selecting cloud services, MCDM-based methods are the most straightforward and effective. In the literature, there are various MCDM-based cloud service selection frameworks. TOPSIS [25], AHP [26], ANP [27], MAUT [28], ELECTRE [29], SAW [30], and rank voting method [31] are the most common MCDM approaches for cloud service selection in the literature. Kumar et al. [25] developed a cloud service selection framework based on AHP and TOPSIS. They adopted a real-time dataset from CloudHarmony and made extensive sensitivity analyses to validate the model’s efficacy. They conclude that the proposed model is effective when compared to other MCDM techniques. Garg et al. [26] created an AHP-based framework to evaluate cloud services based on various applications depending on QoS requirements. Such a framework can create healthy competition among Cloud providers to satisfy their Service Level Agreement (SLA) and improve their QoS. Tripathi et al. [27] incorporated the analytic network process (ANP) into the ranking component of the SMI framework. The interactions among the criteria in this method are used to rank cloud services. The proposed model’s limitation is the number of selection criteria; if this number grows too large, it becomes difficult to keep track of all the interactions between them. Dyer [28] presents a summary of multiattribute utility theory and discusses the problem of multiattribute decisions. Dyer explores the use of multiattribute preference functions under uncertain and risky conditions to decompose them into additive and multiplicative forms. Various forms of multi-attribute preference functions are studied in relation to one another. The relationships between these various types of multi-attribute preference functions are investigated. Govindan et al. [29] thoroughly reviewed English scholarly articles on ELECTRE and ELECTRE-based approaches. This comprises application areas, method modifications, comparisons with other methods, and general research of the ELECTRE methods. The review includes 686 publications in all. Afshari et al. [30] presented an MCDM methodology for Personnel selection. It considers a real application of personnel selection with using the opinion of an expert by one of the decision-making models; it is called the SAW method. The limitation is that it ignores the fuzziness of the executive’s judgment during the decision-making process. Baranwal et al. [31] identified several new QoS measures and described them to allow both the user and the provider to quantify their expectations and offers. They also proposed a dynamic and adaptable methodology that uses a form of the ranked voting method to analyze customers’ needs and recommend the best cloud service provider. Case studies validate the suggested model’s validity and effectiveness. Recent studies have used AHP to evaluate a variety of SaaS services [32,33], IaaS services [34,35], and general cloud services [36,37]. Saaty’s basic 1-9 scale is commonly used to aid users in comparing and evaluating cloud service alternatives. The SMICLOUD framework was developed by Garg et al. [26] to compare and rank three IaaS cloud services using the SMI criteria [38]. According to this paper, the Cloud Service Measurement Initiative Consortium (CSMIC) has determined a set of metrics for measuring the QoS criteria, using which several CSPs are compared. Based on user preferences values, AHP is utilized to compute the weights for criteria, and then these weights are used to compare the three IaaS cloud services. CSPs were only selected based on the quantitative CSMIC criteria without recognizing the non-quantifiable QoS trustworthiness. Godse et al. [39] developed an AHP methodology to rank SaaS services, considering functionality, architecture, usability, vendor reputation, and pricing. Despite the usefulness of AHP, it fails to account for uncertainty in decisions when determining pairwise comparisons. A fuzzy AHP was developed to handle this issue, allowing decision-makers to use fuzzy ranking instead of precise ranking [40]. TOPSIS was used to rank alternatives according to the weights of criteria and alternatives determined by pairwise comparisons applied by AHP. They used the proposed method to assess the trustworthiness of 15 CSPs from several perspectives based on 9 QoS criteria (cost, speed, storage capacity, availability, response time, features, technical support, and ease of use). As a result of our analysis of these papers, we discovered that CSPs were evaluated based on several criteria, which led to more complex pairwise comparisons. Furthermore, most of these criteria are qualitative, resulting in inconsistent results in comparisons and, therefore, less reliable conclusions. This paper proposes a cloud service selection framework based on integrating BOM and TOPSIS methods for selecting the best CSP. In terms of computational complexity and consistency, the proposed framework outperformed AHP, making it more computationally efficient and perfectly consistent.

4  The Proposed Approach

This paper presents an integrated MCDM framework for selecting cloud computing services. The proposed framework incorporates the BOM method, which is used to calculate criteria weights and the relative weights of alternatives relative to each criterion, and TOPSIS, which uses these weights to produce the ranking for cloud alternatives (CSPs). Using the BOM approach, the decision-maker only determines the best criterion before evaluating that criterion against other criteria through pairwise comparisons. By doing so, all of the matrix’s elements meet the property in (9), and all of its judgments are perfectly consistent. Fig. 2 depicts a flow chart summarizing the steps of the integrated framework.

Figure 2: A flowchart showing the stages of the proposed framework

Step 1: (Identify criteria that meet the business needs): Assume that the set of criteria considered is C={c1,c2,⋯,cn}. The number n represents the number of criteria.

Step 2: (Identify the appropriate set of CSPs): Assume that the set of CSPs considered is SP={sp1,sp2,⋯,spm}. The number m represents the number of CSPs.

Step 3: (Identify the best criterion in the set of criteria): Assume that the best criterion selected by the decision-maker is CB where CB ∈ C.

Step 4: (Estimate the values of the pairwise comparison of the best criterion to the others): Assume that the vector CriB represents the comparison values of the best criterion with the remaining criteria in C.

Step 5: (Calculate the appropriate weights for each criterion): Assume that C_W is the vector of size n that contains the weight values of each criterion in C. Obtaining the weight values requires solving the following problem:

wBwj=aBjforallj≠BandaBj∈CriB,j=1,2,3,…,n.(22)

∑j=1nwj=1(23)

Step 6: (Determine the first criterion): Suppose that the first criterion is c1 where c1 ∈ C.

Step 7: (Select the best CSP relative to c1): Suppose the best CSP is SPB the SPB ∈ SP.

Step 8: (Set the values of pairwise comparisons of the best CSP relative to c1): Assume that the vector CSPB represents the pairwise comparison values of the best CSP to other providers in the set SP w.r.t. c1.

Step 9: (Calculate the weight values of the CSPs w.r.t. c1): To obtain the weight values of the CSPs, the following problem should be solved:

wBwi=aBiforalli≠BandaBi∈CSPB,i=1,2,3,…,m.(24)

∑i=1mwi=1(25)

Step 10: (Calculate the weights of CSPs concerning all other remaining criteria): For all remaining criteria, repeat steps 7 through 9.

Step 11: (Develop the matrix of CSP weights): The matrix SP_W of size m×n represents the CSP weights. In this matrix, each column represents the weight values of the CSPs based on the criterion that corresponds to that column. This matrix represents the normalized decision matrix used by TOPSIS.

Step 12: (Compute the weighted normalized decision matrix H): H is calculated using Eq. (12) by multiplying the weight values of the criteria C_Wj by the corresponding columns in the normalized decision matrix (SP_W).

Step 13:(Calculate the positive ideal solution (PIS) and negative ideal solution (NIS)): For every criterion cj, find the positive ideal solution xj+ and the negative ideal solution xj−, where:

xj+=max(h1j,h2j,….,hmj)(26)

xj−=min(h1j,h2j,….,hmj)(27)

Then, compute the PIS and NIS values using Eqs. (17) and (18).

Step 14: (Calculate the Euclidian distance Ei+ and Ei− of each alternative from PIS and NIS): The Euclidian distance Ei+ and Ei− for each criterion is calculated using Eqs. (19) and (20), respectively.

Step 15: (Calculate the closeness value for each alternative (CVi)): The closeness value for each alternative CVi is calculated using Eq. (21).

Step 16: (Rank the alternatives in descending order of the closeness value). The best alternative is the one with the highest closeness value.

5  Experimental Results

A use-case model was employed to analyze and validate the proposed framework, which proved its validity and efficacy.

Step 1. (Identify criteria that meet the business needs): Nine criteria were selected based on the SMI model, where C={c1,c2,c3,c4,c5,c6,c7,c8,c9} and n = 9. Tab. 2 shows the set of selected criteria.

Step 2. (Identify the appropriate set of CSPs): For our use-case model, eight hypothetical CSPs were chosen, where SP={sp1,sp2,sp3,sp4,sp5,sp6,sp7,sp8} and m = 8.

Step 3. (Identify the best criterion in the set of criteria): Assume that the best criterion chosen by the decision-maker is the cost. So, CB= C4.

Step 4. (Estimate the values of the pairwise comparison of the best criterion to the others): It is the responsibility of the decision-maker to determine the pairwise comparison values between each of the criteria in the set and the selected best criterion (CB−to−others), shown in Tab. 3.

Step 5. (Calculate the appropriate weights for each criterion). Tab. 4 shows the weight values of the set of criteria, which are computed using Eqs. (22) and (23), respectively.

The values from Tab. 4 are stored in the vector (C_W) as follows:

C_W=(0.03930.11780.07070.35350.08840.05050.05890.17670.0442)

Step 6. (Determine the first criterion).

Step 7. (Select the best CSPrelative to c1): Assume that SP5 was chosen by the decision-maker.

Step 8. (Set the values of pairwise comparisons of the best CSP relative to c1): The comparison values of SP5 relative to c1(SP5−to−others) is stated by the decision-maker and shown in Tab. 5.

Step 9. (Calculate the weight values of the CSPs w.r.t. c1):

Tab. 6 shows the weight values of the CSPs w.r.t. c1 computed using Eqs. (24) and (25).

Step 10. (Calculate the weights of CSPs concerning all other remaining criteria): For all remaining criteria, repeat steps 7 through 9. In Tab. 7, the The (SPB−to−others) comparison values w.r.t. each criterion are presented in tabular format. In our use-case model, there are nine criteria (columns) and eight CSPs (rows). The decision-maker determines which CSP is the best for each of the criteria and estimates the values of pairwise comparisons of each CSP relative to the others. In Tab. 7, Each shaded cell represents the optimal CSP based on the criterion.

Step 11. (Develop the matrix of CSP weights): In Tab. 8, each column contains the CSPs weights for each criterion.

The values from Tab. 8 are represented in the normalized decision matrix (SP_W) as follows:

SP_W=(0.12680.39410.09640.09510.07880.12860.05430.04930.09640.04230.04330.08010.04750.04950.40070.06340.06930.05720.06680.04140.09200.10020.18610.07360.40070.07450.12260.19020.19710.06430.38040.13140.05510.04750.05630.07710.09510.08670.06680.19020.34670.04450.38040.17330.10020.08010.04650.36790.05010.06200.18400.05720.09310.06130.04230.06340.04930.04380.09640.38570.12680.05430.17330.05780.05010.20030.04450.20030.37230.12410.05260.0460)

Step 12: (Compute the weighted normalized decision matrix H ): H is calculated using Eq. (12) by multiplying the weight values of the criteria C_Wj by the corresponding columns in the normalized decision matrix (SP_W).

H=(0.00500.4640.00680.00370.00930.00910.00210.00580.00680.01490.00380.00400.01680.00440.02020.02240.00610.00290.00390.00730.00410.00590.03290.00330.02360.01320.00540.00750.02320.00450.01490.01550.00390.00190.00660.00550.03360.00770.00340.06720.03060.00220.13450.01530.00510.00470.00820.01630.00300.01100.00810.00340.01640.00270.00170.00250.00580.00520.00680.02730.04480.01920.01530.00510.00250.01010.00260.01180.06580.02190.00230.0020)

Step 13:(Calculate the positive ideal solution (PIS) and negative ideal solution (NIS)): The vectors PIS and MIS are calculated using equations 13 through 18, and the results are as follow:

PIS=(0.01490.04640.02730.13450.03060.02020.02360.06580.0163) NIS=(0.00170.00520.00390.01490.00380.00220.00260.00730.0020)

Step 14:(Calculate the Euclidian distance Ei+ and Ei− of each alternative from PIS and NIS): The Euclidian distance Ei+ and Ei− of each criterion is calculated and shown in Tab. 9.

Step 15: (Calculate the closeness value for each alternative (CVi)): The closeness value for each alternative CVi is calculated and shown in Tab. 9.

Step 16: (Rank the alternatives in descending order of the closeness value). Tab. 9 shows the final CSP ranking.

6  Evaluation

Several measures of the viability of the proposed framework have been considered: computing efficiency (In terms of the number of comparisons made between all pairs) and consistency ratio (CR). Validation was achieved by comparing it with the AHP technique. The exact configuration was used in our comparison experiments for the developed framework and the AHP technique. The AHP computations were carried out using the method presented in [41].

6.1 Computation Efficiency

We calculated the number of pairwise comparisons given by the decision-maker to assess the efficiency of the proposed framework. Nine criteria and eight CSPs were used in all of our experiments. In Tab. 10, we compare the number of comparisons in AHP with those in the developed framework. In contrast with AHP, our proposed framework does not require as many comparisons, thus making it more efficient. It is in part because the proposed framework uses a vector-based approach rather than a matrix-based approach such as AHP, which requires fewer comparisons. For AHP, n×(n−1)/2 comparisons are needed, while for the developed framework, only n−1 comparisons are needed. Fig. 3 illustrates the computational complexity of AHP in contrast to the developed framework. Compared with AHP, the proposed framework requires fewer pairwise comparisons, which implies a reduction in computational effort.

Figure 3: Computational complexity of AHP, BWM, and BOM

6.2 Consistency Ratio (CR)

The reliability of MCDM results is based on the value of the consistency ratio. In our experiment, the CR is calculated using the AHP technique and the proposed framework to evaluate consistency. Tab. 11 compares the CR results of the proposed framework and the AHP technique. For AHP, CR is calculated using Eq. (8). According to the AHP technique, if the comparisons have consistency ratio values greater than or equal to 0.1, they are considered inconsistent.

Based on the eigenvalue theory, if the value of λmax=n, then the pairwise comparison matrix (or vector) is considered entirely consistent. This means that the developed framework is always entirely consistent (CR = 0). Therefore, it is a more reliable and consistent framework in comparison to AHP.

6.3 Analysis and Discussion

We have evaluated and ranked eight CSPs (m = 8) based on nine criteria (n = 9), driven by the decision-makers preferences. The proposed framework was compared to a well-known MCDM method, AHP, using the same configurations to validate the proposed framework’s efficiency and consistency. AHP requires ten matrices: one of size 9x9 determines the weight values of criteria, and nine other matrices of size 8x8 determine the weight values of CSPs relative to each of the criteria. According to the AHP method, the decision-maker should estimate 9×(9−1)/2+9×8×(8−1)/2=288 comparisons. The proposed framework requires only ten vectors: one vector of size 1x9 to calculate the weight values of criteria and nine vectors of size 1x8 to calculate the weight values of CSPs w.r.t.each criterion. According to our developed framework, the decision-maker should estimate (9−1)+9×(8−1)=71 comparisons. Thus, the proposed framework only requires 25% of the comparisons required by the AHP approach. Moreover, the proposed framework is fully consistent since the decision-maker only uses the best criterion (or best CSP) to estimate the values of pairwise comparisons. According to the obtained results, the proposed framework has a CR of 0%, whereas AHP has a CR of 38%. As with AHP, one limitation of the proposed framework is that the accuracy of the decision depends on the estimations done by the decision-maker for the values of the pairwise comparisons of qualitative criteria.

7  Conclusion

This paper proposed an integrated MCDM framework to enable cloud service customers to select the most appropriate CSP by utilizing the BOM and the TOPSIS methods. A formal evaluation and verification of the proposed framework were conducted utilizing a use-case model to validate its effectiveness and consistency. A comparison was made between the proposed framework and AHP. In terms of computing complexity and consistency, our proposed framework performs superior to AHP. Similar to AHP, the proposed framework has the drawback that it relies on decision-makers’ judgments of the pairwise comparison values for qualitative criteria to reach the final ranking list of CSPs. In the future, this work can be extended to include group decision-making.

Funding Statement: The author received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

References

 1.  A. Nayyar, Handbook of Cloud Computing: Basic to Advance Research on the Concepts and Design of Cloud Computing, 1st ed., New Delhi, India: BPB Publications, 2019.

 2.  R. K. Tiwari and R. Kumar, “A robust and efficient MCDM-based framework for cloud service selection using modified TOPSIS,” International Journal of Cloud Applications and Computing, vol. 11, no. 1, pp. 21–51, 2020.

 3.  R. Buyya, C. S. Yeo, S. Venugopal, J. Broberg and I. Brandic, “Cloud computing and emerging IT platforms: Vision, hype, and reality for delivering computing as the 5th utility,” Future Generation Computer Systems, vol. 25, no. 6, pp. 599–616, 2009.

 4.  S. Li, G. Wang and J. Yang, “Survey on cloud model based similarity measure of uncertain concepts,” CAAI Transactions on Intelligence Technology, vol. 4, no. 4, pp. 223–230, 2019.

 5.  S. Namasudra and P. Roy, “A new table based protocol for data accessing in cloud computing,” Journal of Information Science and Engineering, vol. 33, no. 3, pp. 585–609, 2017.

 6.  S. Ahmad, S. Mehfuz and J. Beg, “Fuzzy TOPSIS-based cloud model to evaluate cloud computing services,” in Lecture Notes in Mechanical Engineering, pp. 37–52, 2021.

 7.  D. Ardagna, G. Casale, M. Ciavotta, J. F. Pérez and W. Wang, “Quality-of-service in cloud computing: Modeling techniques and their applications,” Journal of Internet Services and Applications, vol. 5, no. 1, pp. 1–17, 2014.

 8.  J. Siegel and J. Perdue, “Cloud services measures for global use: The Service Measurement Index (SMI),” in Annual SRII Global Conf., San Jose, California, USA, pp. 411–415, 2012.

 9.  I. Grgurević and G. Kordić, “Multi-criteria decision-making in cloud service selection and adoption,” in Proc. of the 5th Int. Virtual Research Conf. in Technical Disciplines, Žilina, Slovak Republic, vol. 5, 2017.

10. L. Sun, “An influence diagram based cloud service selection approach in dynamic cloud marketplaces,” Cluster Computing, vol. 22, no. 3, pp. 7369–7378, 2019.

11. N. Gobi and A. Rathinavelu, “Analyzing cloud based reviews for product ranking using feature based clustering algorithm,” Cluster Computing, vol. 22, no. 3, pp. 6977–6984, 2019.

12. H. M. Alabool and A. K. bin Mahmood, “A novel evaluation framework for improving trust level of Infrastructure as a Service,” Cluster Computing, vol. 19, no. 1, pp. 389–410, 2016.

13. T. L. Saaty, “How to make a decision: The analytic hierarchy process,” European Journal of Operational Research, vol. 48, no. 1, pp. 9–26, 1990.

14. T. L. Saaty, “A scaling method for priorities in hierarchical structures,” Journal of Mathematical Psychology, vol. 15, no. 3, pp. 234–281, 1977.

15. T. L. Saaty, “Axiomatic foundation of the analytic hierarchy process,” Management Science, vol. 32, no. 7, pp. 841–855, 1986.

16. A. Jadhav and R. Sonar, “Analytic hierarchy process (AHPweighted scoring method (WSMand hybrid knowledge based system (HKBS) for software selection: A comparative study,” in Second Int. Conf. on Emerging Trends in Engineering & Technology, Nagpur, Maharashtra, India, pp. 991–997, 2009.

17. R. V. Rao, “Introduction to multiple attribute decision-making (MADM) methods,” in Decision Making in the Manufacturing Environment, pp. 27–41, 2007.

18. M. W. Herman and W. W. Koczkodaj, “A Monte Carlo study of pairwise comparison,” Information Processing Letters, vol. 57, no. 1, pp. 25–29, 1996.

19. R. W. Saaty, “The analytic hierarchy process-what it is and how it is used,” Mathematical Modelling, vol. 9, no. 3–5, pp. 161–176, 1987.

20. R. H. Ansah, S. Sorooshian and S. bin Mustafa, “Analytic hierarchy process decision making algorithm,” Global Journal of Pure and Applied Mathematics, vol. 11, no. 4, pp. 2403–2410, 2015.

21. A. E. Youssef, “An integrated MCDM approach for cloud service selection based on TOPSIS and BWM,” IEEE Access, vol. 8, pp. 71851–71865, 2020.

22. R. Gavade, “Multi-Criteria Decision Making: An overview of different selection problems and methods,” International Journal of Computer Science and Information Technologies, vol. 5, no. 4, pp. 5643–5646, 2014.

23. A. Bahurmoz, “The analytic hierarchy process: A methodology for win-win management,” Journal of King Abdulaziz University-Economics and Administration, vol. 20, no. 1, pp. 3–16, 2006.

24. C.-L. Hwang and K. Yoon, “Methods for multiple attribute decision making,” in Multiple Attribute Decision Making. Berlin, Heidelberg: Springer, pp. 58–191, 1981.

25. R. R. Kumar, S. Mishra and C. Kumar, “A novel framework for cloud service evaluation and selection using hybrid MCDM methods,” Arabian Journal for Science and Engineering, vol. 43, no. 12, pp. 7015–7030, 2018.

26. S. K. Garg, S. Versteeg and R. Buyya, “A framework for ranking of cloud computing services,” Future Generation Computer Systems, vol. 29, no. 4, pp. 1012–1023, 2013.

27. A. Tripathi, I. Pathak and D. P. Vidyarthi, “Integration of analytic network process with service measurement index framework for cloud service provider selection,” Concurrency and Computation: Practice and Experience, vol. 29, no. 12, pp. 1–16, 2017.

28. J. S. Dyer, “MAUT-multiattribute utility theory,” in International Series in Operations Research and Management Science. Vol. 78. New York, NY, USA: Springer, pp. 265–292, 2005.

29. K. Govindan and M. B. Jepsen, “ELECTRE: A comprehensive literature review on methodologies and applications,” European Journal of Operational Research, vol. 250, no. 1, pp. 1–29, 2016.

30. A. Afshari, M. Mojahed and R. Yusuff, “Simple additive weighting approach to personnel selection problem,” International Journal of Innovation, Management and Technology, vol. 1, no. 5, pp. 511–515, 2010.

31. G. Baranwal and D. P. Vidyarthi, “A cloud service selection model using improved ranked voting method, Concurrency and Computation,” Practice and Experience, vol. 28, no. 13, pp. 3540–3567, 2016.

32. R. Karim, C. Ding and A. Miri, “An end-to-end QoS mapping approach for cloud service selection,” in IEEE Ninth World Congress on Services, pp. 341–348, 2013.

33. N. Boussoualim and Y. Aklouf, “Evaluation and selection of SaaS product based on user preferences,” in Third Int. Conf. on Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE), Lebanon, pp. 299–308, 2015.

34. Z. U. Rehman, O. K. Hussain and F. K. Hussain, “Multi-Criteria IaaS service selection based on QoS history,” in IEEE 27th Int. Conf. on Advanced Information Networking and Applications (AINA), Barcelona, Spain, pp. 1129–1135, 2013.

35. Z. U. Rehman, O. K. Hussain and F. K. Hussain, “Iaas cloud selection using MCDM methods,” in IEEE Ninth Int. Conf. on E-business Engineering, Hangzhou, China, pp. 246–251, 2012.

36. R. R. Kumar, M. Shameem, R. Khanam and C. Kumar, “A hybrid evaluation framework for QoS based service selection and ranking in cloud environment,” in 15th IEEE India Council Int. Conf. (INDICON), Coimbatore, India, pp. 1–6, 2018.

37. A. Hussain, J. Chun and M. Khan, “A novel framework towards viable Cloud Service Selection as a Service (CSSaaS) under a fuzzy environment,” Future Generation Computer Systems, vol. 104, pp. 74–91, 2020.

38. S. K. Garg, S. Versteeg and R. Buyya, “SMICloud: A framework for comparing and ranking cloud services,” in Fourth IEEE Int. Conf. on Utility and Cloud Computing, Melbourne, Australia, pp. 210–218, 2011.

39. M. Godse and S. Mulik, “An approach for selecting Software-as-a-Service (SaaS) product,” in IEEE Int. Conf. on Cloud Computing, Bangalore, India, pp. 155–158, 2009.

40. M. Enea and T. Piazza, “Project selection by constrained fuzzy AHP,” Fuzzy Optimization and Decision Making, vol. 3, no. 1, pp. 39–62, 2004.

41. K. Goepel, “Implementation of an Online software tool for the Analytic Hierarchy Process (AHP-OS),” International Journal of the Analytic Hierarchy Process, vol. 10, no. 3, pp. 469–487, 2018.

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