e brand [20] [21] . It has been an important element for customers to choose their cloud service providers.

4. Rough Set Theory

Rough set theory proposed by Pawlark in [22] is a mathematical approach to uncertain knowledge. Rough set theory has been applied in many interesting areas. The rough set approach is of fundamental importance to artificial intelligence and cognitive sciences, especially in the fields of machine learning, knowledge acquisition, knowledge discovery, decision analysis, expert systems, inductive reasoning and pattern recognition [23] . The main advantage of rough set theory in the process of knowledge analysis is based on dataset rather than subjective judgment.

Definition 1 [22] [24] [25] . Let be an information system, where is the finite set of objects; is the set of attributes, C is a conditional attributes set, D is the decision attribute set; where is the set of values of attributes. f is an information function and denotes the map of, which means a value to each attribute for each object.

Definition 2 [22] [24] [25] . Given an information system,. The expression, called a positive region of the partition U/D with respect to condition attributes C, is the set of all elements of U that can be uniquely classified to blocks of the partition U/D, by means of C. U/D indicates elementary concepts of information system T about decision attribute set D. For, we have:

a) If, then is an unnecessary attribute of C;

b) If, then is a necessary attribute of C.

Definition 3 [22] [24] [25] . Given an information system,. Attribute importance of the decision information system can be tested by the classification ability for T when removing an attribute from condition attribute set C, the significance of the attribute is defined by [22] as in:

(1)

Card presents the set cardinality of the attributes. represents the dependence of decision attribute D relative to condition attribute, and which reflects the classification discrimination ability of the attribute. The larger value of, the more stronger of dependency relationships between condition attribute and decision attribute D, and the more discriminative the attribute is.

5. The Cloud Service Selection Method with Preference Information

Cloud users usually give the subjective weight to different parameters of the cloud service based on personal preference when they are choosing the cloud service, thus resulting into non practical choices. Therefore, in this section we introduce an approach to rank the importance of the cloud service indexes and provide the objective weight about different parameters based on the rough set theory.

5.1. The Objective Ranking of Attributes Approach Based on Rough Set Theory

Rough set theory analysis is based on upper and lower approximations space. The lower approximation of the set can describe the precise knowledge in an information system, which is called positive region and is defined by Definition 2. If the lower approximation will not be changed when an attribute is deleted, then the attribute is unnecessary and can be reduced. Otherwise, the attribute is called core attribute, which is necessary. In other words, the Definition 2 can distinguish the core attributes and unnecessary attributes while ignoring the effect of the relatively necessary attributes. For all relatively necessary attributes, we can rank them in an information system according to the significance values of different attributes. The significance of an attribute defined by Definition 3 can reflect the variety of the lower approximation space when the attribute is deleted.

Since cloud service is characterized by various parameters, such as availability or scalability, elasticity and so on, it is difficult to define selection criteria valid for different customer needs. For this problem, we give a cloud service selection method using rough set theory to help user make decision.

We construct an information system based on a large preference datasets collected from users of certain cloud service providers (google, Alibaba et al). Table 2 is an assessment and requirement system of users about the cloud services. U represents the cloud services set,; Condition attributes set represents the assessment parameters of cloud services, C = {availability, scalability, reliability, credit, …, loads}, that is; decision attribute set is satisfied with the cloud service or not, D = {Yes, No}, that is, {1, 0}, where, * represents incomplete information.

Figure 1. Getting the preference information.

Table 1. The preference levels of users.

To obtain the parameters importance of cloud service, the ranking of attributes algorithm as follows:

5.2. Application of the Objective Ranking of Attributes Approach in Cloud Service Selection

Choosing the cloud services is a multiple attributes decision making problem, and the key is to determine the weight of parameters. There are several ways to determine the weight of indicators, on general, which fall into two categories: subjective and objective assignment methods. The subjective assignment method is assigning weight based on subjective information of decision-making. It is arbitrary with poor accuracy and reliability of decision-making. In the objective assignment method, each parameter is evaluated with the actual data. In cloud service selection system, the importance of attributes is different. The objective weight of attributes can be defined as in (2):

(2)

The comprehensive weight with regard to parameters can be defined as in (3):

(3)

where, which is called weight coefficient reflects cloud user preference for subjective and objective weights of parameter when they make decisions in cloud services selection. and respectively represents the weight of parameters of cloud services with objective dataset and subjective dataset. Smaller value of indicates that users value more their subjective preference. Conversely, higher value of users emphasizes the objective importance of parameters. Specially, if, users judging the parameters’ importance of cloud services totally depend on their subjective awareness; if, users completely rely on the objective weight.

Figure 2. Application model of the objective ranking of attributes.

5.3. Application of Attributes Ranking Approach in Cloud Service Selection

There are corresponding indexes designed to evaluate a system or a service. When cloud service providers launch a service product to consumers, they should provide quality of services and they hope to get the feedback from consumers early to improve their products, at the same time, the evaluation indexes of the services to be design accordingly. For cloud service users, when they choose a cloud service, they will consider some factors to obtain the suitable service, such as cloud service availability, cloud service elasticity, brand of service etc. As we know, in economical market, the cost control and the pursuit of efficiency are the primary goals of each company management. The reason cloud users choose moving their business to cloud computing center is because this is a good way to save capital and improve efficiency compare to their traditional development model. However, in practice, cloud users should balance the weight of factors used to evaluate cloud service.

Here we demonstrate an instance to use rough set theory to rank the factors of cloud service providers because the overall strength of cloud service provider is important for cloud users to choose the suitable cloud service. The real data in Table 3 is the list of cloud service providers according to their all-round capacity in 2014. The cloud service providers operate in China. The data is published in the journal of China Internet Weekly [26] . In Table 3, the factors CI (capacity for innovation), SC (service capability), PT (product technologies), S (solution), TCO (total cost of ownership) and BI (Brand influence) are the evaluation factors of cloud service providers. The factor CS (comprehensive score) is the assessment result of the cloud service providers.

In rough set theory, every cloud service provider is represented as a research object, and the factors as its attributes. Among them, the factor CS is decision attribute, while others are condition attributes. Simply, columns of Table 3 are attributes and rows are objects, whereas entries of the table are attribute values. Thus, each row of the table can be seen as information about specific cloud service provider. Our research purpose is to rank the weight of the factors to assess the comprehensive strength of cloud service providers.

In order to decide the weight of factors of cloud service providers to assess their comprehensive strength, we can get the attributes rank and weight values of Table 3 by the ranking of attributes algorithm we proposed which are shown in Table 4. It shows that the factor S is very important than other factors when the given parameters are used for evaluating cloud service providers. The weights of the factor TCO and BI are the smallest ones. They are not the key factors. According to the result of ranking factors, we able to reduce flexibly the evaluation factors.

5.4. An Example of Application of the Objective Ranking of Attributes Approach in Cloud Service Selection

We give an example to explain how to apply our model with personal preference. Table 5 and Table 6 are two information systems respectively based on the user preference dataset and the third-party objective dataset. To distinguish cloud service elements of subjective dataset and objective dataset, we use sj(j = 1, 2, ∙∙∙, 9) and ek(k = 1, 2, …, 20) to represent respectively the cloud service elements in Table 5 and Table 6. Attribute i(i = 1, 2, 3, 4) represents various parameters of cloud services. The value of attribute d is used to show the different decision results per cloud service. They are shown as follows.

Table 3. The scores of cloud service providers.

Table 4. The ranking and weight of attributes.

Table 5. Users’ preference information dataset.

Table 6. Third party objective dataset.

We can get the attributes rank, significance and weight values of Table 5 and Table 6 by Definition 2, 3 and Equation (2), or we get the result integrating Algorithm 1 and Equation (2). The results are shown in Table 7. According to Equation (3), we can obtain the attributes ranking of cloud services with different values of weight coefficient β shown in Table 8.

6. Experiments Result and Analysis

The experiment has two goals. The first one aims for sorting the parameters of cloud services according to their significance to guide the new cloud service users to make decision. The second one aims to prove the method is effective in the application of the cloud services selection with preference information. Due to lack of the related standard test platform of users’ preference and the standard test datasets, here we adopt data sets (download from the UCI [27] ) as the training samples to carry out. Besides that, the original datasets are pre-processed to be easily used for calculating and program designing.

Table 9 shows the basic information of the data sets. Programming code is by Java language. It is executed sequentially on a processor Intel Core2 Duo CPUs x64. The main function of the algorithm is to give the importance order of the attributes. We can get the comprehensive weights of attributes according to the result of ranking and significance of attributes. We can get the ranking attributes by setting the different values of weight coefficient β. Thus we compare to the services matching rate successfully. The experiment regards the objective datasets as the benchmark for analysis to draw graphic. Services matching is used to describe the intention of the selection of cloud users for cloud services providers. We can get the result shown in Figure 3.

Table 7. The ranking, significance and weight of attributes.

Table 8. Ranking for attributes selection.

Table 9. Basic information of test datasets.

Figure 3. Cloud services match-making with various value of β.

It can be seen from Figure 3 that with weight coefficient β greater, users’ subjective preference becomes important, and the service match-making rate decreases; rather, combining the subjective data and objective data, the cloud service match-making rate increases.

The users with the different subjective preference of the attribute weight use the random data to get the subjective service matching rate. As mentioned above, we use the rough set methods to get the objective weight of the attribute, integrating the objective and subjective weight to get the comprehensive matching rate of the service. Here, we set weight coefficient β is 0.1, 0.3, 0.5, 0.7 and 0.9 separately. The results are shown in Figure 4.

We can see in Figure 4, when the datasets have less service objects, the comprehensive selection or subjective selection has high service matching rate successfully. With the data increases, the comprehensive weight matching rate increases, whereas the cloud service match-making rate decreases based on the subjective preference information.

In [12] , the author proposed an analytical framework to explore the significant factors affecting the adoption of SaaS for enterprise users using rough set theory. The main contribution is to mine the important factors. Although our work is similar it in context, but our study goes to one step further, mining the significant factors in assessing cloud service providers (shown in Table 3), for example. There are six factors (CI, SC, PT, S, TCO, BI) in the information system of cloud service provider. It can mine four factors (CI, SC, PT, S) which are the important influence factors for evaluating the cloud service providers using the approach in [12] . Beyond that, we can’t get the additional information about the result. However, in our study, we not only can know which factor is the important evaluation index of cloud service provider assessment but also rank them according to their weight, as the result shown in Table 6. Further, we can define a threshold to select evaluation factors at a stretch based on the result to design the evaluation system. In Table 6, we suppose that, for some reason, we need to reduce the number of evaluation factors from 6 to 4. The method in [12] and ours both are effective. That is, the factors TCO and BI would be removed because their influence is smaller than others for evaluating cloud service providers. And if, we need to reduce the number of evaluation factors from 6 to 3, first, we remove the two factors (TCO, BI), after that, we don’t know which factor would be removed among the other four factors (CI, SC, PT, S, TCO, BI) based on the approach in [12] , because there is no more information to guide us to do further. Therefore, the method proposed in [12] is failed in this case. However, in our work, beside removing the two factors (TCO, BI), we can judge easily to remove the factor (CI), because its weight is lower than the other factors’, or according to the rank of factors importance shown in Table 6.

7. Conclusion

To provide a guide choosing the appropriate cloud services for cloud users, we present the rank-making of the parameters importance in cloud services selection and propose a attribute ranking method based on the rough

Figure 4. Cloud service match-making with varies datasets.

Cite this paper
Liu, Y. , Esseghir, M. and Boulahia, L. (2016) Evaluation of Parameters Importance in Cloud Service Selection Using Rough Sets. Applied Mathematics, 7, 527-541. doi: 10.4236/am.2016.76049.
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