Assessment of cloud service trusted state based on fuzzy entropy and Markov chain

Abstract

In the era of cloud service popularization, the trustworthiness of service is particularly important. If users cannot prevent the potential trustworthiness problem of the service during long-term use, once the trustworthiness problem occurs, it will cause significant losses. In order to objectively assess the cloud service trustworthiness, and predict its change, this paper establishes a special hierarchical model of cloud service trustworthiness attributes. This paper proposes corresponding management countermeasures around the model, defines the cloud service trustworthiness level, defines the cloud service trusted state based on fuzzy entropy and Markov chain, constructs the membership function of the cloud service trusted state, and realizes the assessment of cloud service trustworthiness and its changes according to the prediction method of Markov chain. Through case analysis and method comparison, it shows that the method proposed in this paper is effective and feasible. This method can provide objective and comprehensive assessment data for the cloud service trustworthiness and its change, makes up the deficiency of fuzzy entropy assessment method. This research has important reference value and significance for the research of cloud service trustworthiness assessment.

Introduction

According to Canalys’ “Cloud Service Analysis Statistics” in November 2022, the global cloud infrastructure service expenditure in the third quarter of 2022 increased by 28% year on year, reaching US $63.1 billion. it is thus clear that global enterprises are using more and more cloud applications, and the range of cloud applications of enterprises is also growing. However, with the popularity of cloud services, cloud service downtime caused by various reasons has become a normal. On October 4, 2021, Facebook, Instagram and WhatsApp, the social media in the United States, experienced a massive outage, which lasted nearly seven hours, and their market value evaporated by 300 billion overnight. On November 16, 2021, Google Cloud, one of the world’s largest cloud service providers, went down, causing many large company websites relying on Google Cloud have to interrupt their services. In December 2021, Amazon had three outages in the same month. it is thus clear that even in the era of cloud popularization, cloud service providers cannot promise 100% that the services they provide will not have problems in the use process. Lack of trust in service providers has become the biggest obstacle for users when choosing cloud services¹.

According to the definition of TCG (Trusted Computing Group) ² a service is considered trustworthy if it always develops towards its expected goals; On the contrary, if a service cannot change towards its predicted goals, then the service is not trustworthy. In order to ensure the trustworthiness of cloud services and meet users’ requirements for cloud service trustworthiness, domestic and foreign scholars have conducted research from different perspectives, including analysis of user trustworthiness requirements, research on cloud service assessment methods, research on cloud service recommendation methods, research on service selection methods, or research on cloud computing resource optimization methods. These studies have addressed issues in user trust needs analysis, service recommendation methods, service selection methods, and cloud computing resource optimization methods. However, these methods did not analyze the trustworthiness of cloud services after being selected or used, that is, did not conduct predictive analysis on changes in cloud service trustworthiness during actual long-term use. Due to the lack of prediction of changes in the trustworthiness of cloud services over long-term use, users will be unable to take preventive measures in advance before trustworthiness problems occur. Once the service suddenly fails to operate normally during use, it will cause unpredictable losses. Therefore, it is necessary to predict and assess the trustworthiness and its changes during long-term use, so as to guide the cloud service trustworthiness towards the expected state through decision adjustments before trustworthiness problems occur.

In order to guide the trustworthiness of cloud services towards the expected state change. This study aims to quantitatively describe the cloud service trustworthiness and its changes, predict and assess the cloud service trustworthiness and its changes, identify the key factors that affect the cloud service trustworthiness changes based on the assessment results, so as to provide detailed data support for the trustworthiness decision-making.

1. Established a trusted attribute hierarchy model for cloud services, and proposed the concept of cloud service trusted state based on fuzzy entropy, effectively described the trustworthiness and its changes of cloud services.

2. Constructed a membership function for the trusted state of cloud services, quantitatively describing the impact of various indicators on the changes in the trusted state of cloud services.

3. Based on Markov chain, implemented the prediction and assessment of cloud service trustworthiness and its changes, providing comprehensive assessment results for the prevention of trustworthiness problems.

The overall organizational structure of this article is as follows.

In section “Introduction”, this chapter describes the necessity of the assessment cloud service trustworthiness and its change, and leads to the research content of this paper;

In section “Related research”, this chapter discusses the domestic and foreign research on trustworthiness assessment, describes the characteristics of different methods, and summarizes the main problems of these methods;

In section “Trusted state of cloud service based on fuzzy entropy and Markov chain”, this chapter establishes a trusted attribute hierarchy model of cloud service with 16 indicators, and proposes corresponding management countermeasures for each indicator. Then, this chapter defines the trustworthiness level of cloud service according to the risk matrix method, and proposes a method to represent the trusted state of cloud service based on fuzzy entropy and Markov chain theory;

In section “Assessment of cloud service trusted state based on fuzzy entropy and Markov chain”, the membership function of cloud service fuzzy entropy is constructed based on the risk matrix, and the calculation method of cloud service trusted state is proposed according to the constructed membership function, thus an effective assessment method of cloud service trusted state is proposed by combining fuzzy entropy and Markov chain;

In section “Case analysis and method comparison”, the proposed assessment method of trusted state is applied to a specific case for analysis and comparison with other assessment methods;

In section “Conclusion”, this chapter summarizes the research work of the full text, and points out that the methods proposed in this paper need to be improved.

Related research

Cloud service is not only referring to SaaS (Software as a Service), but also IaaS (Infrastructure as a Service) and PaaS (Platform as a Service). What is closely related to cloud service trustworthiness is service quality, security and reliability. TCG (trusted computing group)² points out that an entity is trusted if it always develops towards the expected goal. ISO/IEC³ defines trustworthiness as the components, operations or processes involved in computing are predictable. In order to comprehensively assess the cloud service trustworthiness, China Communications Standardization Association has proposed the standard YDB 144–2014⁴, which points out the key to the trustworthiness assessment, including the cloud service capabilities, the cloud service security, and the operation and maintenance capabilities of service providers. As for how to conduct trustworthiness assessment, Shen et al.⁵ pointed out that the following three aspects should be carried out, including the establishment of attribute model, the study of evidence model and the definition of trustworthiness level.

In order to ensure that the services provided can meet the trustworthiness needs of users, Chuan⁶ propose to use image blur information to evaluate users’ needs and expectations in cloud service trustworthiness, Tang et al.⁷ proposes a two-dimensional time aware hybrid cloud service recommendation method based on network similarity and trust enhancement. In order to ensure the stable operation of the service, Tofighy⁸, Salimian⁹ and Shahidinejad¹⁰ have proposed different solutions from the perspective of optimizing computing resources, aiming to improve the quality of the service by optimizing computing resources. From the perspective of service selection, in response to the problem of difficult optimization of service composition, Arani et al.¹¹propose a linear programming approach to web service composition problem which is called ‘LP-WSC’, for selecting the most efficient service for each request in a geographically distributed cloud environment to improve service quality standards. These methods have solved the problem of user trustworthiness requirement analysis, optimized the computing resources of services, and improved the accuracy of service selection and recommendation. These methods solve the problem of user trustworthiness requirement analysis, optimize the computing resources of services, and improve the accuracy of service selection and recommendation. However, these methods do not provide predictive analysis for potential cloud service trustworthiness problems that may occur in long-time use, nor do they provide quantitative references for users on how to avoid such problems.

In addition to the above research, relevant scholars have also proposed many effective assessment methods for the security or reliability of cloud service. The method based on AHP (analytic hierarchy process)^12–18 provides model support for the trustworthiness assessment of cloud service, and can ensure the objectivity of the assessment results to a certain extent. However, this single model-based assessment lacks the analysis of changes in cloud service trustworthiness. The uncertainty assessment method based on information entropy^19–23 is an effective method to measure the trustworthiness of cloud service. However, the assessment result of this method only describes the uncertainty of risk, and does not give an estimate for the change of service trustworthiness. The assessment method based on D-S evidence theory^24–28 can effectively solve the problem of information conflict in the assessment process, but this method needs to collect a lot of assessment evidence. The assessment method based on risk matrix^29,30 can give an intuitive level for the trustworthiness of cloud service, but it is obviously insufficient in objectivity. The trusted computing method based on trusted chain^31–33 is an integrity detection method, which focuses on detecting system quality problems and does not comprehensively analyze other factors. The prediction and assessment method based on Bayesian network^34–36 can effectively predict the trustworthiness of cloud service under the condition of having sufficient known data. However, how to reduce the gap between the assessment results and the real data is a problem that needs attention in this method. Using the above methods, domestic and foreign scholars have carried out research on cloud service trustworthiness, either based on service QoS parameters^37–39, or based on user feedback⁴⁰, or based on third-party monitoring data^41,42. Among them, the assessment based on QoS assessment only focuses on quality of service; The assessment based on user feedback evaluation has high requirements for the accumulation of historical data; The assessment based on third-party supervision or assessment data, needs to establish a special monitoring mechanism and requires high costs.

Through the above related research, it is thus clear that any single method or single angle analysis will have its defects in the trustworthiness assessment of cloud service, and they are not fully competent for the assessment of cloud service trustworthiness and its change. To achieve an effective assessment of cloud service trustworthiness and its change, only by combining relevant methods and using the advantages of different methods to deal with the corresponding key issues in cloud service trustworthiness assessment research, can the entire assessment research work be carried out smoothly.

Therefore, around the assessment contents and problems mentioned in the related research, this paper will establish the cloud service trustworthiness assessment attribute model, study the cloud service trustworthiness and its change based on the fuzzy entropy theory, propose the concept of trusted state, and combine Markov chain to realize the assessment of the cloud service trusted state and its change.

Trusted state of cloud service based on fuzzy entropy and Markov chain

Using trusted state instead of trustworthiness level to describe cloud service trustworthiness can more objectively describe the actual trustworthiness. When assessing the cloud service trustworthiness, experts cannot directly assess the trustworthiness of the entire cloud service. In order to effectively assess the cloud service trustworthiness, this paper first establishes a trustworthiness attribute model of cloud service, which will help experts to assess the trustworthiness of the entire cloud service from the bottom up.

Trustworthiness attribute model of cloud service

According to the standard YDB144-2014¹⁰ proposed by China Communications Standardization Association, this paper divides the cloud service trustworthiness into three classes , namely, the trustworthiness of service providers’ operation and maintenance, the trustworthiness of service data, and the trustworthiness of service quality. Around these 3 trustworthiness classes , this paper further combs out 16 important indicators that affect the cloud service trustworthiness through literature review and expert visits. Finally, the trustworthiness attribute model of cloud service is established. The model is shown in Fig. 1.

Fig. 1.

The trustworthiness attribute model of cloud service.

The cloud service trustworthiness attribute model proposed in this paper includes 3 classes and 16 indicators. The meaning of each indicator is shown in Table 1.

Table 1.

Meaning of cloud service trustworthiness assessment indicators.

	Meaning	Countermeasure
	The service change and termination terms formulated by the service provider, which are used to regulate the conditions and procedures for changing and terminating the relationship between the service provider and cloud users.	Before providing or using cloud services, the notification method shall be agreed in advance to ensure that both parties can notify each other as soon as possible.
	Indemnity clause formulated by service providers. The more detailed the indemnity clause, the higher the trustworthiness of the service.	Before providing or using cloud services, compensation terms should be clearly defined, including indemnity matters, indemnity methods, indemnity amounts, etc.
	The exemption clauses formulated by the service provider, such as the interpretation of force majeure factors and exemption scenarios.	Users shall ensure that they can accept the exemption clauses of the service provider.
	Service providers’ constraints on user permissions and application scenarios. The smaller the constraint on users, the higher the service trustworthiness.	Users should check whether the relevant constraints will limit their subsequent application extensions.
	The probability that data will not be lost during the service contract period. The smaller the probability of data loss, the higher the trustworthiness.	Users should make their own database backups every day and back up data to different devices.
	Refers to the portability of data. If the data can be fully migrated, then the credibility is highest.	Users should minimize the dependence of application data on the server system environment.
	The effectiveness of data encryption or isolation processing by service providers. The higher the encryption level of data, the higher the credibility.	Users should detect their own application vulnerabilities and require the service provider to provide an encrypted transmission mechanism.
	Refers to the user’s right to know, about the location of data storage and the usage of service provider data. The greater the user’s legitimate right to know, the higher the trustworthiness.	Users need to clarify the authority of the service provider and prevent data leakage caused by malicious employees inside the service provider.
	When the user needs to review the data, the service provider can provide the data to the user. The more detailed the data that can support the review, the higher the trustworthiness.	Users need to agree with the service provider on the audit data they can provide, and make their own log records for key operations.
	The extent to which data can be destroyed. If the data can be completely destroyed, the trustworthiness is high.	The user needs to agree with the service provider which data must be deleted and the deadline for deletion.
	The actual network bandwidth that the service can reach. The greater the network bandwidth, the higher the service trustworthiness.	Service providers need to clearly explain the cost of increasing network bandwidth and the minimum number of online users that bandwidth can support.
	The capability of service failure recovery. The faster the failure recovery, the higher the service trustworthiness.	Users shall set up alternative servers for possible service failures to ensure the operation of basic functions.
	The functions of the service. The more complete the function, the higher the service trustworthiness.	Before purchase or use, users should judge whether the service function can meet the current and subsequent business needs.
	The time when the service can operate normally. The longer the service can operate normally during use, the higher the trustworthiness.	The user shall make clear whether there is regular maintenance or overhaul time for the service.
	The deployment capability of calculates resource. The higher the feasibility of expanding or reducing computing resources, the higher the service trustworthiness.	Users should investigate whether the service has the ability to expand or reduce computing resources, and determine the time required.
	Measurement of the computing resources. The more accurate the measurement, the higher the service trustworthiness.	For some special metering services, such as SMS verification and message push, users should make their own statistics. Service providers should provide measurement details for their services.

After establishing the model shown in Fig. 1, this paper will study the cloud service trustworthiness level.

Trustworthiness level of cloud service

According to the definition of TCG¹, a service is trusted if it always develops in the expected direction; On the contrary, if a service cannot continue to run normally due to a trustworthiness problem, the service is not trusted. Therefore, in order to quantitatively describe the service trustworthiness and further describe the service trusted state, this paper will classify the trustworthiness level from the trustworthiness problem frequency and the loss severity. As shown in Table 2, this paper defines the trustworthiness problem frequency level and the loss severity level .

Table 2.

Frequency level and loss severity level.

Frequency Level	Meaning	Loss Severity Level	Meaning
5	Ineluctable	5	Catastrophic loss
4	Frequent	4	Very serious loss
3	Occasional	3	Serious loss
2	Rarer	2	Losses to be considered
1	Almost impossible	1	Negligible loss

In Table 2, indicates the trustworthiness problems frequency level in the long-term operation of cloud service. The higher the value of , the higher the frequency of cloud service trustworthiness problems. Similarly, represents the trustworthiness problems frequency level of class , represents the trustworthiness problems frequency level of .

indicates the cloud service loss severity level during long-term operation. The higher the value of , the greater the damage caused by the cloud service trustworthiness problem. Similarly, represents the loss severity level of class , represents the loss severity level of .

After defining the trustworthiness level of cloud service, this paper will continue to study the trusted state representation method of cloud service.

The trusted state representation method of cloud service

It is known that the cloud service trustworthiness is a concept which is difficult to define, and it always changes randomly in the long-term use process. It is not objective to describe the cloud service trustworthiness only with a fixed trustworthiness level. In order to more accurately describe the cloud service trustworthiness, this paper divides the cloud service trustworthiness into 4 states according to the trustworthiness level from high to low. The 4 states are extremely trusted state ,basic trusted state ,critical trusted state and untrusted .

• Extremely trusted state :it means that the service is extremely trusted. The frequency level is extremely low, and the loss severity level is extremely low;

• Basic trusted state :this indicates that the service is basically trusted, and the frequency level and the loss severity level are both general;

• Critical trusted state :this indicates that the service is at the edge of trusted state. The frequency level and the loss severity level are higher than normal;

• Untrusted :it means that the service is untrusted. The frequency level is extremely high, and the loss severity level is extremely high.

Substitute the above 4 trusted states into the risk matrix, as shown in Table 3.

Table 3.

Division of the cloud service trusted state regions based on risk matrix.

	5()	10()	15()	20()	25()
	4()	8()	12()	16()	20()
	3()	6()	9()	12()	15()
	2()	4()	6()	8()	10()
	1()	2()	3()	4()	5)

In Table 3, respectively represent the 4 trusted states. However, in the actual use of cloud service, due to various factors, the trustworthiness of cloud service always changes randomly, that is, it always switches between different trusted states. In order to effectively describe the randomness of cloud service trustworthiness, this paper, based on Markov chain principle⁴³, treats the change of cloud service trustworthiness as a random process, and proposes the concept of trusted state matrix, as shown in the following matrix.

refers to the trusted state matrix of cloud service. The element in the matrix represents the probability of cloud service trustworthiness transferring from trusted state to trusted state ,. This matrix effectively describes the change of the cloud services trusted state in the process of long-term use in a mathematical way. Compared with the fixed trustworthiness level representation method, this matrix can more accurately reflect the actual cloud service trustworthiness and its change.

As mentioned above, this paper proposes an effective trusted state representation method. To calculate the matrix, it needs to calculate the value of of each element in the matrix. In this regard, then this paper will propose an effective calculation method of cloud service trusted state matrix based on fuzzy entropy theory, and further realize the assessment of cloud service trusted state.

Assessment of cloud service trusted state based on fuzzy entropy and Markov chain

In order to carry out the assessment of cloud service trustworthiness based on fuzzy entropy, this paper defines the domain of discourse, fuzzy sets, fuzzy variables, membership and fuzzy entropy of cloud service trustworthiness in turn according to the fuzzy entropy theory, as described below.

Fuzzy entropy of cloud service trusted state

According to the fuzzy entropy theory, this paper regards the trustworthiness environment of cloud service as the research domain , and puts forward 4 trusted states are regarded as four 4 sets of cloud service trustworthiness. contains 16 fuzzy variables, , which are respectively the 16 trustworthiness indicators shown in Table 1. is the membership of the trusted state fuzzy set of cloud service, which indicates the degree of possibility that belongs to the fuzzy set , and its interval is .The greater the value of , the higher the possibility that indicator belongs to .Substitute into the fuzzy entropy calculation formula to calculate, the trusted state fuzzy entropy of can be obtained, as shown in Eq. (1).

1

In Eq. (1), represents the total number of trustworthiness indicators included in , is a constant, . In order to normalize the assessment results, this paper sets the value of as . is the fuzzy entropy of , which indicates the degree of fuzziness that belongs to , .In addition to Eq. (1), according to the definition of fuzzy entropy, fuzzy entropy can also be calculated by Eq. (2).

2

In Eq. (2), represents the probability that belongs to state , and represents the probability that does not belong to state .When , whether belongs to is clearly defined, indicating that clearly belongs to or does not belong to , that is, or .On the contrary, the greater the value of , the greater the fuzzy degree that belongs to , that is, the closer the values of and are.After calculating the value of , the fuzzy degree ranking of can be obtained, as shown in the following example.

Suppose that the ranking of is . This ranking indicates that the fuzzy degree that belongs to is the greatest, that is, the closer the values of and are. On the contrary, the fuzzy degree that belongs to is the lowest, which means that the difference between and is large.

Membership function of cloud service trusted state fuzzy set

According to Eq. (1), to calculate the fuzzy entropy of the trusted state of cloud service, it is necessary to calculate , that is, to construct the membership function of the trusted state fuzzy set.In this regard, according to the division of trusted states in Table 3, combined with the fuzzy entropy theory, this paper constructs the membership function of the cloud service trusted state fuzzy set, as shown in Eq. (3).

3

In Eq. (3), represents the geometric area of trusted state , and, represents the geometric area of . The geometric meaning of Eq. (3) is shown in Fig. 2. As shown in Fig. 2, is composed of intervals and of indicator . Among them, and respectively refer to the minimum and maximum trustworthiness problems frequency levels of indicator , while and respectively refer to the minimum and maximum trustworthiness problems loss severity levels of indicator . Their values can be obtained by experts’ assessment according to the definition in Table 2.

• In Fig. 2, represents the maximum trustworthiness problem occurrence frequency level of , and represents the minimum trustworthiness problem occurrence frequency level of . represents the maximum loss severity level of , and represents the minimum loss severity level of ;

• In Fig. 2, the intersection of and means the possibility that belongs to , and the value of is equal to the intersection of and divided by the geometric area of ;

• If , it means that the possibility of belonging to is .

Fig. 2.

Geometric meaning of membership function of trusted state fuzzy set.

As mentioned above, this paper proposes the concepts of maximum level and minimum level. With this method, experts do not need to give an exact value for or during the assessment of indicator at the third layer in Fig. 1.As long as the interval and of each indicator are given according to the definition of Table 2, the value of can be calculated according to Eq. (3).Next, substitute into Eq. (2), of each trustworthiness class at the second layer can be calculated.The above method reduces the difficulty of expert assessment, and realizes the bottom-up cloud service trustworthiness assessment.

As shown in Fig. 2, assuming the expert assesses and gives the and of indicator as and , respectively. The area composed of and is , occupying a total of 9 squares. Through observation, it can be seen that this trustworthiness indicator may belong to 4 random states: , , , and , where , , , .

Computing method of cloud service trusted state

Although the fuzzy entropy can be calculated through the membership function proposed in section “Membership function of cloud service trusted state fuzzy set”, can only describe the fuzzy degree that belongs to , which is not enough to objectively describe the cloud service trustworthiness and its change in the actual operation process. Therefore, this paper will further study the calculation method of cloud service trusted state based on the proposed fuzzy membership function, so as to realize the assessment of cloud service trustworthiness and its change by combining the trusted state matrix and fuzzy entropy.

It is known that during the use of cloud service, the trustworthiness of will change between different states due to the impact of the indicator it contains. In addition, it is known that represents the probability that indicator belongs to trusted state .

, it indicates that may belong to .Therefore, the trusted state matrix of trustworthiness class can be calculated by comprehensively calculating of each indicator , as shown in Eq. (4).

4

In Eq. (4), represents the probability that trusted state of transferring from to due to the influence of , , . represents the total number of indicators contained in .The calculation of and are shown in Eq. (3), which represents the possibility of the indicator belonging to trusted state and .

For example, when and , take = 1, 2, 3, and 4 respectively, then the values of and can be calculated according to Eq. (4).

Therefore, the following matrix can be obtained according to Eq. (4).

Next, normalize the elements in each row of the above matrix, the trusted state matrix of can be obtained, as shown below.

represents the trusted state matrix of . The element represents the probability that transferring from state to . The sum of elements in each row .After the matrix is obtained, combined with the fuzzy entropy , the trusted state assessment of can be realized.

According to Eq. (2), describes the fuzzy degree that belongs to . The greater the value of , the closer the values of and are, indicating that trusted state is more difficult to control. Therefore, in the assessment process, it is necessary to focus on the two cases that belongs to or does not belong to . In view of these two cases, the trusted state change trend of can be assessed in combination with matrix . As described in the following example.

For example, if the value of a cloud service is the highest, it means that have the highest possibility belonging to or not. Therefore, in order to further effectively assess ’s trustworthiness and its change, it is necessary to focus on the two cases of belonging to or not.

• When belongs to , the trusted state change trend of can be assessed according to the 2nd row elements in matrix ;

• When does not belong to , the trusted state change trend of can be assessed according to other row elements in matrix .

In addition, after getting , the trusted state of cloud service can be regarded as a random change process according to the Markov chain³⁸, and can be regarded as the random state transition matrix of cloud service. Assume that the probability that belongs to different trusted states at time $t$ is and respectively, .According to the prediction method of Markov chain, the change of trusted state at the next time can be predicted, as shown in Eq. (5).

5

According to the Markov chain principle, after a long enough time, that is, after a sufficient number of transfers as shown in Eq. (5), the trusted state of will eventually become stable. Therefore, according to Eq. (5), the trusted state change of can be effectively predicted, and the cloud service trustworthiness can be further assessed by combining fuzzy entropy and matrix .

Assessment process of cloud service trusted state

According to the above analysis, when the trusted state matrix of cloud service is calculated, combined with fuzzy entropy , the trusted state of each trustworthiness class can be assessed. The whole assessment process is shown in Fig. 3.

Fig. 3.

Assessment process of cloud service trusted state.

As shown in Fig. 3, this paper proposes a cloud service trusted state assessment method based on fuzzy entropy and Markov chain. The steps of the whole process are shown below.

Step 1. Assess the indicators of the bottom layer according to the definition shown in Table 2, and calculate the occurrence frequency level interval and loss severity level interval of . The calculation time complexity of the steps will increase linearly with the increase of the number of trustworthiness indicators , so its time complexity is .

Step 2. Substitute and into Eq. (3), and calculate the membership degree . The calculation time complexity is .

Step 3. Substitute into Eq. (2) for calculation to obtain . The calculation time complexity of the steps also will increase linearly with the increase of the number of indicators, so its time complexity is .

Step 4. Substitute into Eq. (4) for calculation to obtain . In Eq. (4), represents the sum of probabilities that trusted state of transferring from to . As mentioned in the previous Sections, this paper proposes a total of 16 trustworthiness assessment indicators and 4 trusted states. According to Eq. (4), to calculate , it is necessary to comprehensively consider the impact of these 16 trusted indicators on the mutual transition of each trusted state. When there are states, this step requires calculations, so the computational time complexity of this step is .

Step 5. Assess the trusted state of and its change in combination with and .

Step 6. According to Eq. (5), predict the trusted state change trend of each trustworthiness class . The calculation time complexity of this step will not be affected by changes in the number of trustworthiness indicators , its calculation time complexity is .

In the whole process, only the bottom indicators need to be assessed, and then the trusted state of and its change can be assessed step by step. The input and output of this method are shown below.

• Input Data: and 。

• Intermediate output Data:

• Output Data:

As mentioned above, this paper defines 4 random trusted states of cloud services based on fuzzy entropy, constructs membership functions for each trustworthiness indicator belonging to different trusted states , quantitatively describes the impact of each trustworthiness indicator on the changes in the cloud service trusted state . Throughout the assessment process, experts only need to provide and for each trustworthiness indicator to calculate the trusted state transition matrix and fuzzy entropy of cloud services , and achieve effective assessment of cloud service trustworthiness and its changes, that is, .

Case analysis and method comparison

Next, in order to verify the feasibility of the proposed method, this paper will put the proposed method into a specific case for analysis.

Case analysis

This paper selects an ECS (Elastic Compute Service) provided by a well-known platform with 2G memory, 4 CPU cores and 2 M network bandwidth. The service provider has been in stable operation for more than 10 years. This paper has investigated the service based on the proposed trustworthiness indicators, and sorted out the indicator information of the service, as shown in Table 4.

Table 4.

Cloud service case.

Indicators	Reference information
Service Agreement termination clauses and exemption clauses.	The service provider has listed clear compensation clauses, service termination clauses and exemption clauses.
User constraints	More user scenarios are restricted, and user permissions are low.
Persistence of data storage	Data storage persistence is up to 99.99%, and data will not be lost.
Data portability	Data portability depends on the user’s own application and cannot be completely migrated.
Data privacy	The service provider does not provide data encryption support, and the data is encrypted by the user himself
Right to know data	The user is not clear about the location and use of data storage.
Data auditability	When it is necessary to review, users can obtain comprehensive operation logs and operation records.
Data destructibility	Server data can be destroyed, but user data cannot be completely destroyed.
Network access performance	The service provider platform only provides basic network defense strategies for the server, and does not provide special DDOS and CC defense support.
Fault recovery capability	If a failure occurs, the service cannot be recovered immediately, and it will take several hours to recover.
Business function	Service providers can provide a large number of services and meet most of users’ business needs.
Business availability	The server can operate normally for a long time, with occasional service failure.
Resource allocation capability	Users can quickly expand or reduce computing resources as required.
Measurement accuracy	The measurement of this service is accurate and almost error free.

According to the steps shown in Fig. 3, this paper first convened 5 experts to assess the trusted indicators of the service, and obtained the data shown in Table 5.

Table 5.

Frequency level and loss severity level of each indicator.

		1	2	4	5
		1	2	3	4
		2	3	2	4
		3	4	2	3
		1	1	4	5
		2	3	3	4
		3	5	3	5
		1	3	1	3
		1	3	1	3
		3	5	3	4
		4	5	1	3
		2	3	2	5
		2	3	3	4
		2	3	2	4
		1	2	1	3
		1	2	1	3

Next, substitute the data in Table 5 into Eq. (3) to obtain the membership of each indicator , as shown in Table 6.

Table 6.

The membership degree of each indicator.

	0.000	0.750	0.250	0.000		0.667	0.333	0.000	0.000
	0.250	0.750	0.000	0.000		0.000	0.167	0.333	0.500
	0.167	0.667	0.167	0.000		0.000	0.500	0.333	0.167
	0.000	0.750	0.250	0.000		0.125	0.500	0.250	0.125
	0.000	1.000	0.000	0.000		0.000	0.750	0.250	0.000
	0.000	0.750	0.250	0.000		0.167	0.667	0.167	0.000
	0.000	0.111	0.222	0.667		0.833	0.167	0.000	0.000
	0.667	0.333	0.000	0.000		0.833	0.167	0.000	0.000

Next, substitute the data of Table 6 into Eq. (2) and Eq. (4), and can be obtained. The results are shown below.

After calculating and , the trusted state of each trustworthiness class will be assessed, as shown below.

Assessment of trustworthiness class β₁

According to the ranking of fuzzy entropy , the value of is the largest, which indicates that has the largest fuzzy degree in state . Therefore, to analyze the trusted state of , it needs to focus on the trusted state changes when belongs to or not.

• In the first case, when belongs to , it can be seen from the 2nd row of the matrix that the probability of still keeping state unchanged is the maximum;

• In the second case, when is in other states, the probability of its transition from other states to is also maximum.

The above results show that in the long-term use of the service, whether belongs to or not, it will always transfer to .

In addition, shows that only transfers between , and .In order to further predict and describe the trusted state change trend of ,this paper assumes that belongs to , and with equal probability, that is, .Next, substitute the above values into Eq. (5),the trusted state change trend of can be predicted, as shown in Fig. 4.

Fig. 4.

Assessment of trustworthiness class

Figure 4 reflects the trusted state change trend of . It can be seen from Fig. 4 that the value of will gradually increase, and the values of and will gradually decrease. This change indicates that the trusted state of will gradually lean towards over time, namely it will gradually change to a safer state over time.

Assessment of trustworthiness class $$ {\varvec{\beta }}_{2}$$

According to the ranking of fuzzy entropy , the value of is the largest, which indicates that has the largest fuzzy degree in state . Therefore, to analyze the trusted state of , it also needs to focus on the trusted state changes when belongs to or not.

• In the first case, when belongs to , it can be seen from the 2nd row of the matrix that the probability of still keeping state unchanged is the maximum;

• In other cases, when belongs to , it will only transfer between and . When belongs to or , it will have a greater probability to transfer to state .

The above results show that will have a certain probability to transfer to the more dangerous state or during the long-term use. In addition, it can be seen from the 4th row of matrix , once have transferred to state , it will be difficult to return to a safer state.

Next, in order to further predict and describe the trusted state change trend of , this paper assumes that belongs to different trusted states with equal probability, .Then, substitute the above values into Eq. (5),the trusted state change trend of can be predicted, as shown in Fig. 5.

Fig. 5.

Assessment of trustworthiness class .

Figure 5 reflects the trusted state change trend of . It can be seen from Fig. 5 that the values of and will gradually increase, and finally . The change indicates that the trusted state of is likely to transfer towards the trusted state of will also shift towards , indicating that has a greater potential trustworthiness risk in the long-term use process.

Assessment of trustworthiness class $$ {\varvec{\beta }}_{3}$$

According to the ranking of fuzzy entropy , the value of is the largest, which indicates that has the largest fuzzy degree in state . Therefore, to analyze the trusted state of , it also needs to focus on the trusted state changes when belongs to or not.

• In the first case, when belongs to , it will have a greater probability to transfer to state or still keeping state unchanged;

• In other cases, when does not belong to , it will transfer towards state in the long-term use process.

Next, in order to effectively predict and describe the trusted state change trend of , this paper assumes that belongs to different trusted states with equal probability, .Then, substitute the above values into Eq. (5),the trusted state change trend of can be predicted, as shown in Fig. 6.

Fig. 6.

Assessment of trustworthiness class .

Figure 6 reflects the trusted state change trend of . It can be seen from Fig. 6 that the values of and will gradually increase, and finally . This change shows that the trustworthiness of shows a good change trend, and will gradually transfer towards or in the long-term use process.

Summary of assessment results

The results of sections “Assessment of trustworthiness class β₁” and “Assessment of trustworthiness class β₃” indicate that the trusted states of and show a good trend of change. Over time, and will transfer towards a more credible state.

The results of section “Assessment of trustworthiness class β₂” shows that of the service has a greater trustworthiness risk. As time goes on, will have a high probability of having a trusted problem, and once a trusted problem occurs, the service will be difficult to return to normal. In Fig. 7, the Membership degree represents the possibility that indicator belongs to the trusted state . The higher the value of , the higher the likelihood that the trusted state of belongs to . If the probability of the indicator belonging to and is higher, it indicates that the indicator may cause the trustworthiness of cloud services to change towards an unfavorable state, resulting in trustworthiness problem.

Fig. 7.

The membership degree of each indicator included in .

It can be seen from Fig. 7 that and are likely to transfer to or , indicating that these two indicators are the key factors affecting the trusted state of . When users select and use this cloud service, they need to focus on the control of and . On the one hand, users need to strengthen the detection of their own application vulnerabilities and require service providers to provide encryption transmission mechanisms; On the other hand, the user needs to agree with the service provider in advance which data must be deleted and the time limit for data deletion, so as to avoid the problem of trustworthiness.

Method comparison

The above case analysis shows the method proposed in this paper is feasible. Next, this paper will compare the proposed method with other mature methods to illustrate the characteristics of this method. These methods are assessment methods based on information entropy^21–23, assessment methods based on AHP^15,16,44, assessment methods based on risk matrix^37,38 and assessment methods based on D-S evidence theory^26–28. These methods are relatively mature assessment methods, which suitable for assessing uncertain systems with multiple objectives.

This paper will continue to use the cloud services shown in Table 4 as a reference, and discuss the characteristics of different methods from five aspects: objectivity, comprehensiveness, cost, scalability, and decision support. Through the comparison with these methods, it will be able to reflect the characteristics of the method proposed in this paper.

• Objectivity. It refers to whether the assessment results can objectively reflect the cloud service trustworthiness. The higher the objectivity, the closer the assessment results are to the real trustworthiness environment.

• Comprehensiveness. It refers to the comprehensiveness of the assessment results. The more assessment results the method can provide, the more comprehensive the method is.

• Cost. It refers to the input of assessment, including the difficulty of expert assessment, number of tasks, difficulty in data acquisition, etc.

• Scalability. It refers to the performance of the method when dealing with new assessment requirements. The higher the scalability, the less adjustment the method needs to make in the face of new assessment requirements.

• Decision support. It refers to the support of assessment results to decision-making. The greater the reference value of the assessment results, the greater the decision support.

Objectivity comparison

It is known that the objectivity of assessment results will be affected by subjective factors and expert opinions, and it needs to be able to effectively reflect the random trusted environment of cloud services. Therefore, in order to visually compare the objectivity of various methods, this paper compares them around the following three aspects. As shown in Table 7.

Table 7.

Objective comparison of each method.

Method	reflect the random trusted environment	reduce the influence of human subjective factors	solve the problem of opinion conflict
Information entropy	No	Yes	Yes
AHP	No	Yes	No
Risk matrix	No	No	No
D-S evidence theory	No	Yes	Yes
The method of this paper	Yes	Yes	Yes

Comprehensiveness comparison

Around the trustworthiness attribute model shown in Fig. 1, this paper compares the comprehensiveness of each method based on the assessment of the following four contents. As shown in Table 8.

Table 8.

Comprehensiveness comparison of each method.

Method	Can assess the trustworthiness of indicator	Can assess the trustworthiness of class	Can assess the trustworthiness of the entire cloud service	Can assess the change of service trusted state
Information entropy	Yes	Yes	Yes	No
AHP	Yes	Yes	Yes	No
Risk matrix	Yes	Yes	No	No
D-S evidence theory	Yes	Yes	Yes	No
The method of this paper	Yes	Yes	Yes	Yes

Cost comparison

As shown in Tables 9 and 10, in order to visually compare the cost of each method, this paper compares the content that needs to be processed and their average time complexity when using different methods for assessment.

Table 9.

Cost comparison of each method.

Method	Need assess the occurrence frequency level and loss severity level of each indicator	Need assess the occurrence frequency level and loss severity level of each class	Need calculate the membership of each indicator	Need calculate the fuzzy entropy and trusted state matrix	Need calculate the service uncertainty	Need calculate the weight judgment matrix of each indicator	Need calculate the weight judgment matrix of each class	Need check the consistency of the assessment results	Need fuse the assessment results of multiple experts
Information entropy	Yes	No	No	No	Yes	No	No	No	No
AHP	No	No	No	No	No	Yes	Yes	Yes	No
Risk matrix	Yes	Yes	No	No	No	No	No	No	No
D-S evidence theory	Yes	No	No	No	No	No	No	No	Yes
The method of this paper	Yes	No	Yes	Yes	No	No	No	No	No

Table 10.

Comparison of the average time complexity of each calculation step in the assessment process of each method.

Method	Assess the occurrence frequency level and loss severity level of each indicator	Assess the occurrence frequency level and loss severity level of each class	Calculate the membership of each indicator	Calculate the fuzzy entropy and trusted state matrix	Calculate the service uncertainty	Calculate the weight judgment matrix of each indicator	Calculate the weight judgment matrix of each class	Check the consistency of the assessment results	Fuse the assessment results of multiple experts
Information entropy		-	-	-		-	-	-	-
AHP	-	-	-	-	-				-
Risk matrix			-	-	-	-	-	-	-
D-S evidence theory		-	-	-	-	-	-	-
The method of this paper		-			-	-	-	-	-

Scalability comparison

Take the service assessed in this paper as a reference. When new indicators are introduced, the scalability of each method is compared as follows. The more content that needs to be recalculated when new assessment indicators are introduced, the lower the scalability of the method. As shown in Table 11.

Table 11.

Scalability comparison of each method.

Method	Content that needs to be recalculated
Information entropy	①The entropy values of new indicators ②The entropy values of different classes ③The service uncertainty
AHP	①The weight judgment matrix of each indicator ②The weight judgment matrix of each class ③The consistency of the assessment results
Risk matrix	①The occurrence frequency level and loss severity level of new indicators ②The occurrence frequency level and loss severity level of each class
D-S evidence theory	①The occurrence frequency level and loss severity level of new indicators ②Refuse the assessment results of multiple experts
The method of this paper	①The occurrence frequency level and loss severity level of new indicators ②The membership of the new indicators ③The fuzzy entropy and trusted state matrix

Decision support comparison

In order to effectively compare the decision support of each method, this paper continues to use the cloud service described in section “Case analysis” as a reference, and compares the content that each method can provide for decision support, as shown in Table 12.

Table 12.

Decision support comparison of each method.

Method	Content that can be provided for decision-making
Information entropy	①The uncertainty of different indicators ②The uncertainty of different classes
AHP	①The trustworthiness impact weights of different indicators ②The trustworthiness impact weights of different classes ③Check the consistency of the assessment results
Risk matrix	①The trustworthiness level of different indicators with strong subjectivity ②The trustworthiness level of different classes with strong subjectivity
D-S evidence theory	①The trustworthiness level of different indicators with certain objectivity ②The trustworthiness level of different classes with certain objectivity
Methods of this paper	①The trustworthiness level of different indicators ②The fuzzy degree of different trustworthiness classes ③The cloud service trusted state change trend

In summary, according to the comparison results in Tables 7, 8, 9, 10, 11 and 12, t is used to compare and describe the characteristics of the above methods. The final comparison result is shown in Fig. 8.

Fig. 8.

Characteristics comparison of each method.

Figure 8 shows that the method proposed in this paper has high objectivity, comprehensiveness and decision support, but its cost is high and its scalability is medium.

Conclusion

This paper establishes a trusted attribute hierarchy model of cloud service based on YDB144-2014 standard. Based on this model, this paper defines the trustworthiness level of cloud service, proposes an effective trusted state representation method, constructs a membership function of the cloud service trusted state based on fuzzy entropy, finally proposes an effective trusted state assessment method of cloud service by combining fuzzy entropy and Markov chain. This paper provides a reference model for the trustworthiness assessment of cloud service, reduces the assessment difficulty of expert by combining the fuzzy entropy theory, and uses the “trusted state” to describe the cloud service trustworthiness and its change in combination with Markov chain. It makes up for the shortcomings of assessment method which only using a single fuzzy entropy in the assessment process, and realizes the assessment of cloud service trustworthiness and its change.

This method combines fuzzy entropy and Markov chain, provides a new method for cloud service trustworthiness assessment, and is of great significance to the research of cloud service trustworthiness assessment. In the subsequent research, with the development of trustworthiness research, when the number of trustworthiness indicators of cloud service increases, the scalability of this method needs to be further improved.

Author contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Jia Wang, Gui Bin and Leijin Long. First draft of the manuscript was written by Ming Yang and Rong Jiang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

This research was supported by the National Natural Science Foundation of China (no. 72261033), Yunnan Fundamental Research Projects (nos. 202101AT070211, 202201AT070142) and the Foundation of Yunnan Key Laboratory of Service Computing (no. YNSC23110).

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Declarations

Competing interests

The authors declare no competing interests.

Ethical statement

I certify that this manuscript is the original and has not been published. During the submission period, it will not be submitted to other places for publication. The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.