Dynamic security in cloud computing based on fuzzy cognitive maps

1 Introduction

In recent years, the computer industry has witnessed the rise in popularity of a new paradigm known as Cloud Computing. Although the concept of Cloud Computing is not new and was first introduced by John McCarthy in 1960 [1], this paradigm has taken off 2002, mostly due to Amazon. As the Cloud had storage and processing capacity greater than his needs, Amazon decided to resell them. As of 2010, Cloud Computing has become the fastest growing segment among business applications and is on its way to becoming the norm for most businesses. Cloud Computing is the current trend that promises a major evolution in computing. Cloud users do not need any knowledge or experience related to the technology behind the services offered according to the IDC research firm “International Data Corporation” [2].

Cloud computing, like any other distributed computing system, is continuously exposed to various threats from numerous sources [3, 4]. Thus, cloud security is now a very important concern for providers and users [5, 6]. Therefore, Cloud Computing can only deliver on its promises with the assurance of a high level of security, accessibility and availability. However, security is often cited as the main barrier to Cloud Computing adoption [7]. The rapid development of this model has created a whole new range of security, and privacy issues, such as information degradation or loss, theft or unauthorized transfer of information, data localization, compliance and compliance maintenance, and issues with sharing technologies.

In the Cloud Computing environment, many researchers are interested in data security in the cloud, such as the research carried out in [1, 8–12]. Due to the importance of Cloud data, these researchers considered that it’s the main resource that must be protected in the cloud. They presented some of the techniques that can be used to protect data. In the cited work [12, 13]; a proposed scheme can be used to protect data stored in the cloud. Our work is based on a detailed study of data security in Cloud Computing. In addition, we propose a new system that allows the assessment of risks of the Cloud data in order to reduce these risks and ensure a higher level of protection.

The system being proposed is built on the qualitative reasoning of Fuzzy Cognitive Maps (FCM). FCMs are a modeling methodology based on the exploitation of knowledge and experience. In 1986, Kosko’s FCM methodology is one of the most significant qualitative soft computing methods [14], as an extension of a cognitive map. The FCM approach is a flexible computational method that provides a powerful and flexible framework for knowledge representation and reasoning and a practical tool for dynamic system modeling.

Like other traditional cognitive maps, FCM is a graph knowledge-based method that is made up of concepts and the causal relationships that connect them. The main difference between FCMs and other models is that FCMs use fuzzy sets to represent concepts, and fuzzy connections to describe their relationships. In other words, the inclusion of fuzzy feedback in the FCM structure offers the possibility of obtaining and modeling causal information. According to [15], FCM may be described by two features. The first one is a particular link between concepts of different intensities that are represented by uncertain fuzzy numbers. The second is system dynamicity, which refers to how the system evolves or changes over time. The main advantage of FCM lies in its ability to incorporate human knowledge and refine it through learning processes [16].

FCMs are an approach that uses both fuzzy logic and artificial neural networks to model complex systems. They are similar to recurrent neural networks and are often used for decision-making and prediction in various fields, including finance, engineering, and medicine. In other words, FCMs are a combination of fuzzy logic, expert systems, and neural networks that serve as a powerful tool for simulating and researching the dynamic behavior of complex systems. As a result, from an Artificial Intelligence (AI) perspective, FCMs can learn according to their dynamic structure. The FCM’s capacity to learn enhances both its computational behavior and structure [16–18].

FCMs have been applied in diverse domains including decision making, agricultural systems, environmental management, control systems, time series forecasting, psychology and behavioral science, classification, education, electrical and software engineering, political science, social science, medicine, engineering, robotics, information technology, and telecommunications, etc [15, 19–22]. These various works are the results of many characteristics it possesses. Among these characteristics, we mention qualitative modeling, ease of perception, high capacity to cope with uncertainties, capability to describe nonlinear and causal processes, flexibility, and explainability [21, 23].

The basic idea of this work is to leverage FCMs in Cloud Computing, particularly in Cloud data security. In the proposed system, the use of FCM qualitative reasoning ensures the coherence of partial decisions (for different threat classes) created during our risk assessment process. It enables us to understand the reasons behind past decisions by analyzing causality. Additionally, they allow us to predict future outcomes based on past data, providing solutions and recommendations to enhance cloud data security by reducing potential risks.

The utilization of FCM for Cloud data risk assessment provides the convenience of analyzing, monitoring, tracking, and predicting the security status of Cloud Computing. In this work, the graphical form of FCMs makes the results obtained more readable and understandable. Generally, Cloud experts aim to minimize the risks of Cloud data to guarantee the best security, which is made possible by developing a new process based on FCM.

In this paper, some fundamental aspects of Cloud Computing and security concerns are discussed. The paper also highlights various types of threats that have been documented in the literature and proposes a novel approach for assessing these threats using FCMs. Additionally, the paper provides an application example that has been integrated into the FCM Expert and MATLAB tool.

So, the principal objective of this paper is to present a new and alternative approach to Cloud data risk assessment through the proposed process. We provide a brief overview of related works in Cloud Computing and FCM domain in sections 2 and 3. In section 4, we will provide motivation and describe the proposed approach. The proposed approach will be implemented and illustrated by some examples in section 5. In section 6, we will present the experimental results. The execution scenario and validation will be shown in section 7. Finally, in section 8, we will conclude this work and provide some perspectives.

2 Cloud computing

Cloud Computing is considered the fifth generation of architecture. Although there are many definitions of Cloud Computing in the literature, there is one that is widely accepted as authoritative, which was issued by the National Institute of Standards and Technology (NIST) [5]. The NIST view of Cloud Computing is based on three service models, four deployment models, and five essential characteristics. The three service models defined by NIST are:

Software as a service (SaaS): the user only controls application configurations (e.g. Google Apps, Salesforce.com);

Generally, there are two key parts of the Cloud Computing model as presented in [25] a front-end, and a back-end. The front end is a representation of the side that users can see, such as the computer and programs. The cloud system is represented by the back end, which is not visible to consumers such the storage media and cloud servers. In addition to the previously mentioned components, the cloud environment is made up of the five layers shown in [10, 26]. These layers include the client layer, which is operated on laptops by cloud users to access cloud services; the application layer is a representation of cloud services and the apps that cloud customers utilize; platform layer which provides the cloud applications; infrastructure layer represents the cloud storage, databases, etc.; and the server layer.

In this paper, we will focus on threats that are likely to affect users in the private cloud, PaaS, and SaaS service models.

3 Fuzzy Cognitive Mapping (FCM)

Hard computing methods are based on quantitative values, which can be expensive and may not accurately represent real-world situations due to uncertainties. On the other hand, soft computing techniques provide an alternative approach for tackling complex problems [35]. To achieve more robust and tractable solutions, soft computing techniques like fuzzy logic, neural networks, evolutionary algorithms or a combination of these are often implemented. A quantitative approach and a qualitative approach are the two methodologies used to model and analyze dynamic systems. Sometimes, modeling complex and nonlinear systems quantitatively can be difficult and expensive [36]. In contrast, the limitations described above do not exist in qualitative approaches [21]. In 1986, Kosko proposed FCMs as an expansion of cognitive maps, which are a type of important qualitative soft computing method. Researchers are very interested in FCM due to its strong capacity to solve complex and dynamic issues [37].

FCM is a method used to simulate complex real-world situations [14, 39]. It can handle both qualitative and quantitative inputs and outputs, making it possible to combine assessments of a problem that are based on both types of data [23, 40]. They can be used to represent different perspectives and draw conclusions about the values and beliefs of different individuals and groups, as well as reflect unique mental models of how the world operates [41].

3.1 Formalization of fuzzy cognitive maps

FCM is a tool that combines fuzzy logic with neural network techniques to handle uncertainties and complex characteristics of different systems. It is a type of cognition network that is developed by experts through an interactive procedure of knowledge acquisition [14, 43].

An FCM is a signed fuzzy weighted digraph that expresses causal relationships between ideas and information at different granularity levels [44]. It is made up of a collection of n linked nodes (C₁, C₂,..., C_n) that represent the variable concepts of the modeled system, such as inputs, outputs, states, and events. Signed weighted arcs are used to connect these nodes and define the causal relationships between them [15]. The dynamics of the model are illustrated by the interactions between these nodes (concepts). Generally, the edge weight W_ij that connects two concepts C_i and C_j is given a value on the interval [–1, 1] to indicate three possible types of relationship [45]: positive causality (W_ij > 0), negative causality (W_ij < 0), or independence (W_ij = 0) between the two nodes. The value of W_ij indicates how strongly concept C_i influences concept C_j [46]. In a weight connection matrix Wn×n, the map is shown. Each row in the matrix represents the causal relationship between concept Ci and all other concepts in the map [44]. In a given iteration, the state vector A1×n denotes the present values of n concepts (nodes). Equation (1) is utilized to calculate the value of each concept by considering the impact of other concepts on the designated concept [46–48]. A i ( t + 1 ) = f ( A i ( t ) + ∑ j = 1 j ≠ i n A j ( t ) × W ji )(1)

Where A i ( t + 1 ) is the value of concept C_i at time (t + 1), A i ( t ) is the value of concept C_i at time step (t), whereas, f () is the threshold or activation function for converting the output of each computation to the range [0,1] or [–1, 1].

Figure 1 shows an example FCM for the data threat class and its adjacency matrix. Ci is a concept with a state value. The state value can be represented as a fuzzy value between 0 and 1, indicating the degree of existence of a concept, or as a binary value of 0 or 1, indicating whether a concept is open or closed.

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Fig. 1

(a) An FCM proposed by Cloud Computing expert and (b) its adjacency matrix.

In the first rule mentioned, the function f () is used to limit the activation value of each concept within the allowed range. This function can take on various forms, such as bivalent, trivalent, hyperbolic tangent, or sigmoid, depending on the specific requirements of the system [49, 50].

Bivalent and trivalent are both discrete and produce a limited number of states. The sigmoid function and the hyperbolic tangent are both members of the continuous group and result in infinite states [21, 51]. According to a benchmarking research conducted by S. Bueno and J. L. Salmeron [49], the sigmoid activation function provides the best performance when compared to other functions.

4 Related works

In recent years, Cloud Computing has attracted the attention of many researchers in different aspects. The security issue considered as a main issue in the Cloud Computing, especially Cloud data security. In 2013, security was the most significant issue in Cloud Computing, as noted by the authors in [52], accounting for 87% of the problems. In 2016, the authors of [27] stated that security was the highest priority, with a value of 66%. From a security perspective, several threats affect the domain of Cloud Computing. Improving cloud data security can be made easier by identifying the nature, level of impact, and purpose of potential threats, according to various researchers. For example, in 2010, the Cloud Security Alliance (CSA) identified the top threats to Cloud Computing. These included abuse and nefarious use of Cloud Computing, insecure interfaces and APIs, malicious insiders, data loss or leakage, account or service hijacking, and insecure interfaces and APIs. Twenty eight cloud security threats were found by the researchers and were grouped into five categories [53]: security standards, network, access control, cloud infrastructure, and data. Network, data, and specific threats to the cloud environment are the three categories into which the researchers divided the top threats to Cloud Computing [32]. In [10], the researchers discussed data breaches, data loss, account or service hijacking, insecure interfaces and APIs, denial-of-service, data location, and malicious insiders as top threats to Cloud Computing. Five different categories of threats were defined by the researchers in [54], whereas 26 threats were provided, together with potential challenges and suggested solutions [25]. Also in another work [24], the different threats are classified into four classes: data threats, access threats, threat specific to the Cloud environment and network threat.

In our work, we have developed a cloud data security risk assessment process based on the latest classification. This process is based on FCMs qualitative reasoning. Not many applications have used FCMs in Cloud Computing yet, but they have demonstrated their effectiveness in other areas: electrical circuits [55], political developments [56], virtual sea world of dolphins, shark and fish [57], organizational behavior and job satisfaction [58], economic demographics of world nations [59], qualitative simulation of construction performance [78], advanced medical decisions [79], the design game-based learning systems [80], business process performance measurement [81], medical and bioinformatics [82], flight control system for quadcopters [76], soft computing approaches for time series forecasting [83], classification of imbalanced data [84], and the cognitive radio networks [85]... etc.

We proposed a new system called Dynamic Security based on Fuzzy Cognitive Maps (DSFCM) to improve Cloud Computing security. Our approach combines the field of Cloud Computing and FCM to assess data risks. In the following sections, we present the advantages of this combination.

5 Towards a dynamic system to assess the cloud security risks

Cloud computing is a rapidly-changing and distributed environment where different entities from various domains need to collaborate dynamically, exchanging and sharing a large amount of personal information efficiently, transparently, and in a scalable manner. Additionally, these entities often interact with each other without prior knowledge.

In order to make data security more scalable and suitable, it is crucial to have dynamic and flexible security management between users and Cloud service providers. The challenge of ensuring the security of information and data in the Cloud persists due to the lack of a reliable security model that meets user requirements. This problem has been addressed in previous studies, but no effective solution has been found.

We have conducted a thorough analysis of the limitations of current security systems, and as a result, we have developed a new security system called SDFCM (Dynamic Security based on Fuzzy Cognitive Maps). This new system is based on FCMs to model data and assess potential risks. The choice to use this paradigm in security modeling was guided by the main interests of FCMs, which can be summarized as follows:

FCM is a qualitative modeling tool used to represent human perception of complex systems in a simple way that all participants can understand.

These different characteristics make FCMs more suitable for modeling security in complex and dynamic environments such as Cloud Computing. In our security system, FCMs are used to calculate the risk degree in the field of Cloud Computing. For example, a high degree of protection of a customer’s database ensures that their information is secure and trustworthy. While a low degree means that most (or all) of the criteria necessary to establish security are not met.

The proposed system describes the process of assessing data risks in the cloud. This process is the result of extensive research [24, 86]. The aim of our work is to propose a cloud risk assessment system using FCMs, a qualitative decision support tool.

Our DSFCM system is designed to ensure and enhance cloud security through three main steps. The first step involves identifying various threats that may exist at the Cloud Computing level. The second step involves calculating the consequences of these threats. Finally, in the last step, we will provide recommendations to reduce the risks. In the following sections, we will elaborate on each step in detail.

5.1 Identifying cloud computing threats

The most crucial step in our cloud data risk assessment system is threat identification (as shown in Fig. 2). In this step, we conducted a thorough and specific search to identify the various threats documented in the literature. We also created the relevant FCMs associated to each threat class.

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Fig. 2

Architecture of the first step in the risk assessment process.

5.1.1 Top threats

In this section, we are based on the most critical threats that exist in Cloud Computing as presented by Cloud Security Alliance and others [24, 30–34]. These threats are classified into four types in this study: data threats, access threats, threat specific to the Cloud environment and network threat.

5.1.2 Construction of the associated FCM

Our research involves the use of FCM theory. It is a type of graph where the nodes are fuzzy sets, and the directed edges of the graph represent causal relationships between the factors. The edges also determine the degree of influence connected to each factor, which is measured as weights. The weight of an edge is either a number from the interval [–1, 1] or a linguistic scale value such as {Low, Medium, High}. These values characterize the strength of influence relevant to the connection or degree of reliance on the presence of this connection.

The methods of analysis used in FCM operations involve the application of fuzzy mathematics. The following is the most commonly used approach for calculating fuzzy influence: suppose that between factors f _i and f _j there are m paths, and I _r (f _i , f _j ) denotes influence of f _i on f _j along r path, and T(f _i , f _j ) aggregate influence of f _i on f _j along all m paths. Then: I r ( f i , f j ) = min w p , p + 1(2) T ( f i , f j ) = max 1 ≤ r ≤ m I r ( f i , f j )(3)

Where w_{p,p  + 1} is the weight of oriented graph of f_p on f_p +1 along the r path. Thereby I_r(f_i, f_j) highlights the most weak connection of f_i on f_j along r path (2), and T(f_i, f_j) highlights the most strong connection in I_r (f_i, f_j) (3). In our approach, the strongest connections in I_r (f_i, f_j) will correspond to probability of threat realization.

As previously mentioned, our security model relies on FCMs to evaluate and mitigate risks associated with Cloud Computing. FCMs are particularly adept at handling security uncertainty in complex systems like the Cloud and are capable of dynamically representing system behavior. There are various techniques employed for building and designing FCMs [60]. These methods can be classified into two categories; deductive methods and inductive or automatic methods. Deductive methods rely on human expertise and domain knowledge, while inductive methods use historical data from a given system to build a FCM model [14].

In our system, we will use a deductive modeling method because our work is based on documents and results from expert knowledge. This step consists of two sub-steps: identification of key security concepts and causal relationships between them.

a. Concepts (threats)

The FCM is modeled as a directed graph labeled G(C, E) where:

C={C1, C2,..., Cn} is the set of concepts that form the nodes of the graph (Table 1).

E: is the set of causal relations shown in the next section.

In compliance with recent studies [24, 86] and the opinion of many domain experts, we have identified a set of threats (concepts) that can cause significant damage to an organization’s data, assets, profitability, and reputation. The most important concept list is presented in Table 1.

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Table 1

The list of FCM concepts associated to our system

b. Causal relationships

The second step to building the FCM consists of determining the influence and the degree of influence of a concept on another concept [39]. The notation of causal relationships is E = {e_ij |i, j ∈ C, E ⊆ C× C}. E is a set of arcs representing the causal links between the nodes of the graph. So, every arc e_ij ∈ E represents a one-way causal relation directed from concept C_i to concept C_j, such that C_i and C_j ∈ C. Each arc e_ij is assigned a weight w_ij ∈ [–1, 1], which expresses the degree of value correlation of the concept C_i to the value of the concept C_j. In FCMs, the weight W_ij can indicate a positive relationship W_ij > 0, negative W_ij < 0 or no relationship between the concepts C_i and C_j (W_ij = 0).

In general, the weights values that correspond to the causal relations between the concepts have an imprecise or uncertain nature and it is difficult to represent them precisely with a mathematical model. In this context, the use of fuzzy logic to express these causal relationships seems more appropriate, as it deals with inaccurate and ambiguous information [61]. Moreover, it allows an element to belong to a set with membership degrees included in the continuous real interval [0, 1], rather than overall {0, 1}. Using this approach, Cloud domain experts can describe the degree of influence of one concept on another by linguistic variables of the set T (influence):

T(influence) = {Very Strong Negative (VSN), Strong Negative (SN), Medium negative (MN), Weak Negative (WN), Zero (Z), Weak Positive (WP), Medium Positive (MP), Strong Positive (SP), Very Strong Positive (VSP)}.

The nine linguistic variables represent the three possible types of influence of one concept on another in FCMs; positive, negative or no influence in the interval U = [–1, 1]. For example, the very strong negative variable (VSN) means “a negative influence less than –75% ”, the variable Zero (Z) means “no influence”, the very strong positive variable (VSP) means “a positive influence greater than 75% ”, etc... In our work, experts do not have to assign numerical values to causal relationships but describe the degree of causality between concepts linguistically. Each expert estimates the values of the causal links between the concepts using the linguistic variables of the set T. Then, all linguistic values proposed for the same weight W_ij, are combined using the SUM operator of fuzzy logic and a global linguistic value is produced. At the end of this step, the center-of-gravity (CoG) defuzzification method is used to calculate the numerical value of W_ij that belongs to the interval [–1,+1] from the global linguistic value obtained [11].

Figure 3. The membership functions of triangular form which corresponds to the linguistic variables of the set T.

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Fig. 3

shows the membership functions of triangular form which corresponds to the linguistic variables of the set T.

In the proposed system, we have based on the opinion of three Cloud domain experts. These experts are invited to build the FCM associated to each class of threats. The fusion of the three developed FCMs is made in order to obtain an FCM modeling each class of threats. The main purpose is to get more accurate results. To understand the process of FCM fusion, e.g. experts (1, 2, 3) propose the respective linguistic values SP, VSP and SP for the same weight W_ij, these linguistic variables (SP, VSP and SP) are summed up and an global linguistic weight is produced. Then, using the CoG method, the global linguistic value is transformed to the numerical value 0.79, as shown in Fig. 4. Using this approach, the weight matrices (connections) can be constructed after determining all the weights of the causal relationships. Finally, note that for each W_ij ∈ Wn×n, if i = j, then W_ij = 0, because we suppose that no concept can influence itself.

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Fig. 4

Aggregation of the three linguistic variables (SP, VSP and SP) using the SUM operator of fuzzy logic.

In our work and according to the detailed study on the various threats that exist at the level of Cloud Computing. We have associated to each class of threats an FCM that allows describing the different causes or the different specific elementary threats. The four resulting FCMs are combined into a global FCM describing all threats in Cloud Computing. The objective of modeling each class of threat alone is to obtain more accurate, realistic, and logical results. To also facilitate the follow-up of the inference process to arrive at the best recommendations that reduces these threats.

5.2 Calculate the consequences

Once the step of constructing the different FCMs is finished, we continue with the step of calculating the consequences (Fig. 5). This step consists of the inference process execution. A very important step before performing this process is to transform each FCM to a matrix form. This form makes it easier to manipulate FCMs in order to apply the inference process.

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Fig. 5

Architecture of the second step of the proposed process.

The inference process used in our work is the same as presented in [37, 63]. Except in the threshold function, we used the sigmoid function. The following algorithm summarizes this inference process.

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Algorithm: Inference process
–Suppose we have a cognitive map of n concepts
1. Extract the adjacency matrix Mij.
2. Prepare exciter vector a1.
/ * Initialize the exciter vector to zero (0). * /
For i = 1 to n do
a1 [i]←0;
endFor
/ * Each value i represents the state of concept i. * /
-Set to 1 the desired concepts.
- Add a1 to Working Memory WM.
i ← 1;
3. While i < = n do
ai +1 = ai×Mij;
If (ai +1 ∈ WM or ou ai +1 - ai < 0.001) then ai +1 is typical behavior.
else For i = 1 to n do
a i + 1 = 1 1 + e λ a 1 + 1
endFor
add ai +1 in WM
endIf
i ← i + 1;
endWhile

6 System testing and results

In this section, we describe the main functionality of the system by presenting the three principal steps as they were described in section 5. In our work, in order to FCMs construction, also inference process execution, we used the FCM Expert tool. In addition, to make simulations, Matlab Simulink is also used.

6.1 Identifying cloud computing threats

The first step is devoted to the FCMs construction used in our system. We based on the threat classification proposed in [24]. This classification makes it possible to group the various threats into four classes. Each class is modeled by a FCM under the FCM Expert platform. The fusion of these different FCMs is a global FCM representing all the existing threats in our field of application which is Cloud Computing.

To fully understand the operation of our system and according to the opinions of experts in the cloud domain, we limit the concepts representing the different classes to the first fourteen concepts shown in Table 1 to facilitate monitoring of the proposed approach to assess the risks of Cloud data.

In order to have a global view of the data risks, a combination of all the FCMs of these threats is made. The result is a global FCM using the “Augmented Topology” function in FCM Expert. Figure 6 shows the global FCM.

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Fig. 6

Result of the inference process execution on the global FCM.

6.3 Elaborate recommendations to reduce risks

The development of recommendations (Fig. 7) is the most important step in our system. The different typical behaviors are transformed to a rule base. In other words, it is simulating the inference results of the FCM Expert platform for each threat. We chose a Mamdani type fuzzy inference system with input and output variables.

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Fig. 7

Architecture of the third step.

Mamdani fuzzy inference is a method to create a control system by synthesizing a set of linguistic control rules obtained from experienced human operators. In a Mamdani system, the output of each rule is a fuzzy set. Mamdani systems have more intuitive and easier to understand rule bases, they are well-suited to expert system applications such is the case in our domain.

For a better simulation of our system, we modeled the inference of all classes of threats: data threat, threat specific to the Cloud environment, access threat, and network threat. Each threat class has its own set of variables.

In our work, we modeled the inference process in FCMs by the inference system under Matlab Simulink to transform the inference results into more logical results for non-specialists. In the following sections, we show the main steps to building each inference system of each threat class.

6.3.1 Fuzzification of input and output variables

•Fuzzification of input variables

The variables vary in an interval (according to the inference table under FCM Expert). According to our needs, we have chosen a domain of variation [–1, 1], and nine triangular type membership functions are laquoVSN [–1, –0.75], SN [–1, –0.5], MN [–0.75, –0.25], WN [–0.5, 0], Z [–0.25, 0.25], WP [0, 0.5], MP [0.25, 0.75], SP [0.5, 1], VSP [0.75, 1]raquo.

•Fuzzification of output variables

We have chosen a domain of variation [0, 1], and five membership functions of triangular type are laquoZ [0, 0.25], WP [0, 0.5], MP [0.25, 0.75], SP [0.5, 1], VSP [0.75, 1]raquo with two parameters.

•Inference rules

The manipulation of symbolic and logical rules has made possible one of the great successes of artificial intelligence. Their objective is, through the manipulation of a large number of rules, to make a judgment on a problem in a specific domain.

•Defuzzification of output variables

The results obtained using the fuzzy logic rules explain each rule and the changes that occur in its domain.

According to these obtained results, the final stage of the risk assessment process involves creating a list of recommendations for reducing the risk level. After a detailed analysis of these results with domain experts, a set of recommended actions for risk reduction is developed. The recommendations are then prioritized, and instructions are provided for eliminating any consequences in case the threat is realized.

7 Execution scenario and validation

7.1 Execution scenario

To fully understand the proposed approach, to clarify, and simplify the system developed, we have chosen the class of data threats as an application example.

7.1.1 Identifying cloud computing threats

The FCM associated to this class of threats is shown in Fig. 8. (a). The initial FCM is created according to the views of the Cloud domain experts.

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Fig. 8

(a): Activation of concepts, (b): Result of the inference process execution for data threats.

7.1.2 Calculate the consequences

In this step, we launched the inference process (Fig. 8 (b)), several iterations were performed. The final values of the concept activation vectors are used to represent the different recommendations. In our work, we use the Sigmoid function with a threshold of “0.5” (Fig. 8 (a)) in order to represent the different levels of risk. High values make it possible to judge this entity worthy of security and thus make the decision to recommend it. However, values those are close to or below zero mean that most or all risks are declining (is the principal aim of our work).

In the inference process execution above, the results show that at each step of activation of the different concepts (threats), there is an increase or decrease in the values of these concepts. This shows that there are strong causal relationships between the different threats. The following figure (Fig. 9) shows the associated table to the inference process under FCM Expert.

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Fig. 9

Associated table to the inference process.

We can summarize these results as follows: when the value of the concepts (C1: availability = 0.8383, C2: security model = 0.679, C3: network security = 0.8944, C5: database security = 0.7567) is increased, the value of the other concepts is decreased (C6: data loss = 0.2897, C8: network attacks = 0.3192). So, according to this scenario, we can deduce that to increase the security of cloud data, we must increase availability (C1), create a more secure model (C2), increase network security (C3), and database security (C5). Also, it is necessary to control the data (C6) and take measures to mitigate network attacks (C8).

7.1.3 Elaborate recommendations to reduce risks

To simulate our work, we chose a fuzzy inference system for the Mamdani type data threat class.

It is essential to define membership functions for both input and output parameters. A membership function (MF) is a fuzzy set that extends the indicator function in classical sets and represents the degree of truth as a valuation extension. An MF (x)=0 indicates the absence of membership, while MF (x)=1 represents a full membership.

In this step, after the fuzzification of the input variables: “Network Security, Database Protection, Encryption, Security Model” and also the fuzzification of the output variable: “Availability, Network Attacks, Data Loss”, we pass to the step of building the inference rules. The latter are of if...then type.

It is necessary to specify a set of rules in the form: IF-THEN. For example, in our case:

if “Network Security” is “VSP”, and “security model” is “VSP”, and/or “database security” is “SP”, then “data loss” is “SN”;

if “Network Security” is “SP”, and “security model” is “SP”, and/or “database security” is “VSP”, then “data loss” is “SN” and “Network Attacks” is “MN”;

if “network security” is “VSN”, and “Encryption ” is “SN”, and/or “security model” is “SN”, then “data loss” is “SP” and “availability ” is “SN”;

if “Encryption ” is “SN”, and “security model” is “VSN”, and/or “database security” is “SN”, then “data loss” is “SP” and “Network Attacks” is “MN”;

To understand the inference rules, we suppose the following example under Matlab:

16. If (Network_Security is VSP) and (Database_Protection is VSP) and (Encryption is VSP) then (Availability is VSP) (Network_Attacks is Z) (Data_Loss is WP).

This rule means: if the value of network security is very strong positive [0.75, 1], database protection is very positive strong [0.75, 1], and also encryption is very strong positive [0.75, 1] then the value of availability is very strong [0.75, 1], network attacks are zero (very small [–0.25, 0.25]), and data loss is weak positive [0, 0.5].

The last step is the defuzzification of the output variables which are availability, network attacks, data loss. At the data threat class level, Fig. 10 shows the results obtained from this defuzzification for the given practical example.

According to the results obtained in Fig. 10, we observed that the security of the Cloud context varies with changes to input variables. In particular, when the value of the network security (0.75), encryption (0.75), and database protection (0.63) concepts increases, then the availability (0.805) of other services increases, and the value of network attacks (0.25) and data loss (0.356) is decreased until a stable phase of the system. Based on our evaluation model, data security can be affected by various factors, including encryption, database protection, and network security. For instance, to minimize network attacks, it is recommended to enhance the degree of encryption, monitor the protection of databases, and implement additional measures to improve network security.

OPEN IN VIEWER

Fig. 10

Defuzzification of output variables.

In the global FCM obtained, we have 25 key concepts representing the different threats. So we have 2 ²⁵ possible scenarios, which are over 33 million possible scenarios. After a logical analysis and translation of these results, and taking in parallel the opinion of experts, our system gives a good recommendations according to the state of the Cloud security entered in the form of a global FCM. The developed system (DSFCM) allows for a comprehensive description of the Cloud’s current state, an estimation of its security level, and the development of solutions that are aligned with the reasoning of human experts. This approach helps to reduce risks and enhance the security of cloud data.

8 Conclusion

This article aims to propose and develop a new Cloud data risk assessment system based on FCM that will help experts in the Cloud Computing field to decide the right recommendations to improve and guarantee the cloud data security. Our system is used to receive the Cloud data security status as the current status of the Cloud Computing platform in the form of FCM. This last is considered as one of the most effective artificial intelligence modeling methods. Indeed, this type of qualitative modeling tools has shown their ability to model uncertainty in complex systems through many previous studies and it seemed appropriate to experiment with them to model security in a complex and dynamic environment which is Cloud Computing. In our work, to elaborate the key concepts and the causal relations of the developed FCMs, we based on the opinion of three Cloud experts and the data of some previous works.

The application of the proposed approach is a new system named DSFCM. This consists of three main steps. The first step is devoted to the identification of threats. In this step, we have identified the different criteria that can influence the level of security for each threat. Also, the FCM for each class of threats is constructed with the degrees of influence between these concepts. The second step is devoted to the calculation of the consequences of these threats, using the FCM Expert platform for the inference process execution. In the last step, a simulation of threats under the MATLAB platform is made, using the fuzzy inference system to develop the various recommendations to reduce the risks of the data in order to ensure good distributed security management and guarantee better traceability of the behavior of the members of the system.

The result of combining FCMs and the Cloud Computing domain is our new system (DSFCM). This system offers the following advantages:

In Cloud Computing risk assessment, how to quantify the probability of risk is one of the most important issues; solving this problem is the main objective of our system;

In order to improve our system, we propose in the future to perform the following tasks:

One of the limitations of the FCM Expert platform is to require the use of ratings (C1, C2, etc.), which makes it difficult to analyze the results obtained more precisely. In this context we propose to add an option to directly write the concepts relating to the domain to be modeled.