A fuzzy group decision-making framework for computer network security evaluation with probabilistic linguistic information

Abstract

The computer network security evaluation is a classical multiple attribute group decision making (MAGDM) problems. Recently, the Exponential TODIM TODIM (ExpTODIM) method has been used to cope with MAGDM issues. The probabilistic linguistic term sets (PLTSs) are used as a tool for characterizing uncertain information during the computer network security evaluation. In this manuscript, the probabilistic linguistic ExpTODIM (PL-ExpTODIM) is built to solve the MAGDM under PLTSs. In the end, a numerical case study for computer network security evaluation is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM TODIM (ExpTODIM) method is extended to the PLTSs; (2) the probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is defined to solve the MAGDM under PLTSs; (3) In the end, a numerical case study for computer network security evaluation is given to validate the proposed method.

Keywords

Multiple attribute group decision making (MAGDM)probabilistic linguistic term sets (PLTSs)information entropy ExpTODIM computer network security evaluation

1. Introduction

With the gradual development of information technology, internet technology and computer technology have also been optimized. At this point, there is an explosive growth in user demand, and in this environment, accurate analysis of the computer network security situation is becoming increasingly important [1, 2, 3]. The number of computer network security incidents is gradually increasing, which has a significant impact on the diversified development of the network [4, 5]. Therefore, in order to efficiently handle network security issues and ensure that computer network systems can work safely and normally, it is necessary to achieve high-precision and efficient computer network security situation analysis. The computer network system is not a linear system and has high chaos and nonlinearity. It cannot directly use the designated function mode to describe the computer network security situation. In order to analyze the computer network security situation with high accuracy, experts at home and abroad use neural networks and time series models to analyze it [6, 7, 8]. The prediction accuracy of such models cannot meet the security requirements of gradually developing computer network systems. This is because computer network traffic is susceptible to interference from factors such as network user behavior and economy, and has attributes such as periodicity and nonlinear changes. Previous prediction models cannot fully grasp the attributes of network traffic changes and fail to comprehensively analyze the network security situation, resulting in low prediction accuracy [9, 10, 11]. With the development of science and technology, computer networks have already become an essential tool in modern society. The storage function of computer networks enables the preservation and dissemination of information resources and network data. Due to the large number and wide range of users in computer networks, as well as the presence of computer hackers in society, the risk of information leakage continues to increase. However, in traditional computer network management solutions, there is a lack of emphasis on computer network information storage management [12, 13, 14]. Therefore, the resources and data of computer networks are difficult to protect. In recent years, the development and use of cloud computing technology have not only changed the social work and living environment, but also promoted the transformation and development of computer network security. Cloud computing technology is a data sharing model centered around the Internet, utilizing various computing methods to aggregate resources and automate management through software [15, 16, 17]. Virtualization, as the most prominent feature of cloud computing technology, enables it to break through the boundaries of time and space. The application of cloud computing technology in computer network security storage should aim to protect the integrity, confidentiality, and usability of data in the network environment, so that the entire computer network system can operate continuously, reliably, and orderly [18, 19, 20]. The diversification and barrier of computer network security itself result in a large number of security interference factors. It is not only affected by factors such as computer intrusion viruses, network system design, and network structure, but also by the lack of network mechanisms and the invasion of hackers. At present, China’s core network security management technologies include network data encryption methods, firewalls, data backup and recovery methods, and intrusion detection methods. Even if such methods can to some extent protect computers from danger, the drawbacks they have in practical use cannot be ignored [21, 22, 23].

Multicriteria Decision Analysis (MCDA) is used to sort or select the optimal alternatives under the existing decision information [24, 25, 26, 27, 28, 29, 30]. It is widely used in energy, politics, environment, commerce and other fields [31, 32, 33, 34, 35]. With the increasing complexity of the multiple attribute group decision making (MAGDM) problems [36, 37, 38, 39], it is of great necessity to consider the DMs’ psychological factors [40]. Tversky and Kahneman [41] built the prospect theory (PT) under risk. Gomes and Lima [42] built the TODIM for MADM issues under risk. Leoneti and Gomes [43] defined the Exponential TODIM (ExpTODIM) method. Sun et al. [44] defined the extended Exp-TODIM method for MADM based on the Z-Wasserstein distance. The computer network security evaluation is classical multiple attribute group decision making (MAGDM). Recently, Exponential TODIM (ExpTODIM) method [43] has been used to cope with MAGDM issues. The PLTSs [45] are used as a tool for characterizing uncertain information during the computer network security evaluation. In this manuscript, we design the probabilistic linguistic ExpTODIM (PL-ExpTODIM) to solve the MAGDM under PLTSs. In the end, a numerical case study for computer network security evaluation is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM TODIM (ExpTODIM) method is extended to the PLTSs; (2) the probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is defined to solve the MAGDM under PLTSs; (3) In the end, a numerical case study for computer network security evaluation is given to validate the proposed method.

The research framework of this paper is listed below. In Section 2, the PLTSs is introduced. In Section 3, probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is designed under PLTSs with entropy. Section 4 gives an illustrative case for computer network security evaluation and some comparative analysis. Some remarks are given in Section 5.

2. Preliminaries

Pang, Wang [45] proposed the PLTSs.

Definition 1 [45]. Let $HL=\{{hl_{\alpha}|{\alpha=-\eta,\ldots,-2,-1,0,1,2,\ldots,\eta}}\}$ be the LTS, the linguistic terms $hl_{\alpha}$ depict the information to $\chi$ along with function $f$ :

$\displaystyle f:[{hl_{-\eta},hl_{\eta}}]\to[{0,1}],f({fl_{\alpha}})=\frac{% \alpha+\eta}{2\eta}=\mu$ (1)

$\mu$ is denoted the same information to the $sl_{\alpha}$ with function $f^{-1}$ :

$\displaystyle f^{-1}:[{0,1}]\to[{hl_{-\theta},hl_{\theta}}],f^{-1}(\mu)=hl_{({% 2\mu-1})\eta}=fl_{\alpha}$ (2)

Definition 2 [45]. Given the LTS $HL=\{{hl_{\alpha}|{\alpha=-\eta,\ldots,-2,-1,0,1,2,\ldots,\eta}}\}$ , a PLTS is defined:

$\displaystyle HL(p)=\left\{{hl^{({h\phi})}({p^{({h\phi})}})\left|{hl^{({h\phi}% )}\in HL,p^{({h\phi})}\geqslant 0,h\phi=1,2,\ldots,\#HL(p),\sum\limits_{\phi=1% }^{\#HL(p)}{p^{({h\phi})}\leqslant 1}}\right.}\right\}$ (3)

where $hl^{({h\phi})}({p^{({h\phi})}})$ is the $h\phi$ th $hl^{({h\phi})}$ with the probability $p^{({h\phi})}$ , and $\#HL(p)$ is the defined length of $HL(p)$ . The $hl^{({h\phi})}$ in $HL(p)$ are given by ascending order.

Pang, Wang [45] normalized the PLTS $HL({hp})$ as

$\displaystyle HL({hp})=\left\{hl^{({h\phi})}({hp^{({h\phi})}})\left|hl^{({h% \phi})}\in HL,hp^{({h\phi})}\geqslant 0,h\phi=1,2,\ldots,\#HL({hp}),\sum% \limits_{h\phi=1}^{\#HL({hp})}{hp^{({h\phi})}=1}\right.\right\},hp^{({h\phi})}% ={p^{({h\phi})}}\left/{\sum\limits_{h\phi=1}^{\#HL(p)}{p^{({h\phi})}}}\right.$

for all $h\phi=1,2,\ldots,\#HL({hp})$ .

Definition 3 [45]. Let $HL=\{{hl_{\alpha}|{\alpha=-\eta,\ldots,-2,-1,0,1,2,\ldots,\eta}}\}$ be the LTS, $HL_{1}({hp})=\{hl_{1}^{({h\phi})}({hp_{1}^{({h\phi})}})|h\phi=1,2,\ldots,\#HL_% {1}({hp})\}$ and $HL_{2}({hp})=\{hl_{2}^{({h\phi})}({hp_{2}^{({h\phi})}})|h\phi=1,2,\ldots,\#HL_% {2}\linebreak({hp})\}$ be two PLTSs, $\#HL_{1}({hp})$ and $\#HL_{2}({hp})$ are the length of $HL_{1}({hp})$ and $HL_{2}({hp})$ . If $\#HL_{1}({hp})>\#HL_{2}({hp})$ , then add $\#HL_{1}({hp})-\#HL_{2}({hp})$ linguistic terms to $HL_{2}({hp})$ . The added linguistic terms are the smallest linguistic term in $HL_{2}({hp})$ and the probabilities are zero.

Definition 4 [46]. Let $HL({hp})=\{{hl^{({h\phi})}({hp^{({h\phi})}})|{h\phi=1,2,\ldots,\#HL_{(}{hp})}}\}$ be LTS. Let $HL_{1}({hp})=\{{hl_{1}^{({h\phi})}({hp_{1}^{({h\phi})}})|{h\phi=1,2,\ldots,\#% HL_{1}({hp})}}\}$ and $HL_{2}({hp})=\{hl_{2}^{({h\phi})}({hp_{2}^{({h\phi})}})|h\phi=1,2,\ldots,\#HL_% {2}\linebreak({hp})\}$ be two PLTSs with $\#HL_{1}({hp})=\#HL_{2}({hp})=\#HL({hp})$ , then probabilistic linguistic Euclidean distance $\textit{PLED}({HL_{1}({hp}),HL_{2}({hp})})$ is defined:

$\displaystyle\textit{PLED}({HL_{1}({hp}),HL_{2}({hp})})=\sqrt{\left.{\sum% \limits_{h\phi=1}^{\#\,HL_{1}({hp})}{({hp_{1}^{({h\phi})}f({hl_{1}^{({h\phi})}% })-hp_{2}^{h(\phi)}f({fl_{2}^{({h\phi})}})})^{2}}}\right/{\#HL({hp})}}$ (4)

Definition 5 [45]. For the $HL({hp})=\{{hl^{({h\phi})}({hp^{({h\phi})}})|{h\phi=1,2,\ldots,\#HL_{(}{hp})}}\}$ , the expected values $EV({HL({hp})})$ and deviation degree $DD({HL({hp})})$ of $HL({hp})$ is:

$\displaystyle EV({HL({hp})})=\left.{\sum\limits_{\phi=1}^{\#HL({fp})}{f({HL({% hp})})hp^{({h\phi})}}}\right/{\sum\limits_{h\phi=1}^{\#HL({hp})}{hp^{({f\phi})% }}}$ (5) $\displaystyle DD({HL({hp})})=\left.{\sqrt{\sum\limits_{h\phi=1}^{\#HL({hp})}{(% {f({HL({hp})})hp^{({h\phi})}-EV({HL({hp})})})^{2}}}}\right/{\sum\limits_{h\phi% =1}^{\#HL({hp})}{hp^{({h\phi})}}}$ (6)

The order relations between two PLTSs is followed: (1) if $EV({HL_{1}({hp})})>EV({HL_{2}({hp})})$ , $HL_{1}\linebreak({hp})>HL_{2}({hp})$ ; (2) if $EV({HL_{1}({hp})})=EV({HL_{2}({hp})})$ , if $DD({HL_{1}({hp})})=DD({HL_{2}({hp})})$ , then $HL_{1}({hp})=HL_{2}({hp})$ ; if $DD({HL_{1}({hp})})<DD({HL_{2}({hp})})$ , then, $HL_{1}({hp})>HL_{2}({hp})$ .

3. PL-ExpTODIM method for PL-MAGDM

In this section, the PL-ExpTODIM method is designed for MAGDM. Let $HA=\{HA_{1},HA_{2},\ldots,\linebreak HA_{m}\}$ , $HG=\{{HG_{1},HG_{2},\ldots,HG_{n}}\}$ be alternatives and attributes set with attribute weight $h w$ , where $hw_{j}\in[{0,1}]$ , $\sum\limits_{j=1}^{n}{hw_{j}}=1$ and a set of experts $HE=\{{HE_{1},HE_{2},\ldots,HE_{q}}\}$ . Suppose that the linguistic information is depicted as: $hl_{ij}^{k}$ . Then, the PL-ExpTODIM method is designed to deal with PL-MAGDM.

3.1 Construct the probabilistic linguistic information

(1) Switch cost attribute into beneficial one. If the cost information is $hl_{\eta}$ , then the beneficial information is $hl_{-\eta}({\eta=-3,-2,-1,0,1,2,3})$ .

(2) Switch the linguistic information $hl_{ij}^{k}$ into PLTs: $hl_{ij}^{({h\phi})}({hp_{ij}^{({h\phi})}}),h\phi=1,2,\ldots,\#HL_{ij}({hp})$ and build the PL-matrix $HL=({HL_{ij}({hp})})_{m\times n}$ , $HL_{ij}(p)=\{{hl_{ij}^{({h\phi})}({p_{ij}^{({h\phi})}})|{h\phi=1,2,\ldots,\#HL% _{ij}(p)}}\}$ .

(3) Obtain the normalized PL-matrix $HL=({HL_{ij}({hp})})_{m\times n}$ , $HL_{ij}({hp})=\{hl_{ij}^{({h\phi})}({hp_{ij}^{({h\phi})}})|h\phi=1,2,% \linebreak\ldots,\#HL_{ij}({hp})\}$ .

3.2 Obtain the attributes weight with information entropy

Entropy [47] is a useful method to obtain weight. Firstly, the normalized PL-matrix $\textit{NHL}_{ij}({hp})$ is designed [48]:

$\displaystyle\textit{NHL}_{ij}({hp})=\frac{EV({HL_{ij}({hp})})}{\sum\limits_{i% =1}^{m}{EV({HL_{ij}({hp})})}},$ (7)

Probabilistic linguistic Shannon information entropy $\textit{PLSIE}=({\textit{PLSIE}_{1},\textit{PLSIE}_{2},\ldots,\textit{PLSIE}_{% n}})$ is designed:

$\displaystyle\textit{PLHIE}_{j}=-\frac{1}{\ln m}\sum\limits_{i=1}^{m}\textit{% NHL}_{ij}({hp})\ln\textit{NHL}_{ij}({hp})$ (8)

and $\textit{NHL}_{ij}({hp})\ln\textit{NHL}_{ij}({hp})=0$ if $\textit{NHL}_{ij}({hp})=0$ .

Then, the weights $hw=({hw_{1},hw_{2},\ldots,hw_{n}})$ is designed:

$\displaystyle hw_{j}=\frac{1-\textit{PLHIE}_{j}}{\sum\limits_{j=1}^{n}{({1-% \textit{PLHIE}_{j}})}},j=1,2,\ldots,n.$ (9)

3.3 PL-ExpTODIM method for PL-MAGDM

In this section, the PL-ExpTODIM method is designed for MAGDM.

(1) Obtain relative weight information:

$\displaystyle\textit{rhw}_{j}={hw_{j}}/{\mathop{\max}\limits_{j}}hw_{j},$ (10)

(2) The probabilistic linguistic dominance degree $\textit{PLDD}_{j}({HA_{i},HA_{t}})$ of $HA_{i}$ over $HA_{t}$ for $HG_{j}$ is designed.

$\displaystyle\textit{PLDD}_{j}({HA_{i},HA_{t}})=\left\{{{\begin{array}[]{ll}{% \frac{\textit{rhw}_{j}\times({1-10^{-\rho\textit{PLED}({HL_{ij}({hp}),HL_{tj}(% {hp})})}})}{\sum\nolimits_{j=1}^{n}{\textit{rhw}_{j}}}}&{\text{if }EV({HL_{ij}% ({hp})})>EV({HL_{tj}({hp})})}\\ 0&{\text{if }EV({HL_{ij}({up})})=EV({HL_{tj}({hp})})}\\ {-\frac{1}{\pi}\frac{\sum\nolimits_{j=1}^{n}{\textit{rhw}_{j}\times({1-10^{-% \rho\textit{PLED}({HL_{ij}({hp}),HL_{tj}({hp})})}})}}{\textit{rhw}_{j}}}&{% \text{if }EV({HL_{ij}({hp})})<EV({HL_{tj}({hp})})}\\ \end{array}}}\right.$ (11)

where $\pi$ is the amplification parameter values according to the findings of Tversky and Kahneman [41] and $\pi\in[{1,5}]$ . When assuming higher values $\rho$ indicates that the curvature of the function more accentuate, which could be sensitive to small variations [43].

The $\textit{PLDD}_{j}({HA_{i}})({j=1,2,\ldots,n})$ with respect to $HG_{j}$ is designed:

$\displaystyle\textit{PLDD}_{j}({HA_{i}})=[{\textit{PLDD}_{j}({HA_{i},HA_{t}})}% ]_{m\times m}{\begin{array}[]{*{20}c}{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;% \;\;\;\;HA_{1}}&{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;HA_{2}}&{\;\;% \;\;\;\;\;\;\;\;\;\;\ldots}&{\;\;\;\;\;\;\;\;\;\;\;HA_{m}}\\ \end{array}}={\begin{array}[]{*{20}c}{HA_{1}}\\ {HA_{2}}\\ \vdots\\ {HA_{m}}\\ \end{array}}\left[{{\begin{array}[]{*{20}c}0&{\textit{PLDD}_{j}({HA_{1},HA_{2}% })}&\ldots&{\textit{PLDD}_{j}({HA_{1},HA_{m}})}\\ {\textit{PLDD}_{j}({HA_{2},HA_{1}})}&0&\ldots&{\textit{PLDD}_{j}({HA_{2},HA_{m% }})}\\ \vdots&\vdots&\ldots&\vdots\\ {\textit{PLDD}_{j}({HA_{m},HA_{1}})}&{\textit{PLDD}_{j}({HA_{m},HA_{2}})}&% \ldots&0\\ \end{array}}}\right]$

(3) Produce the $\textit{PLDD}_{j}({HA_{i}})$ of $HA_{i}$ over other alternatives for $HA_{t}$ :

$\displaystyle\textit{PLDD}({HA_{i},HA_{t}})=\sum\limits_{j=1}^{n}{\textit{PLDD% }_{j}({HA_{i},HA_{t}})}$ (12)

The $\textit{PLDD}=({\textit{PLDD}_{it}})_{m\times m}$ is defined:

$\displaystyle\textit{PLDD}=({\textit{PLDD}_{it}})_{m\times m}$ $\displaystyle\quad=\left[{{\begin{array}[]{*{20}c}&{HA_{1}}&{HA_{2}}&\ldots&{% HA_{m}}\\ {HA_{1}}&{\sum\limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{1},HA_{1}})}}&{\sum% \limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{1},HA_{2}})}}&\ldots&{\sum\limits_{j=% 1}^{n}{\textit{PLDD}_{j}({HA_{1},HA_{m}})}}\\ {HA_{2}}&{\sum\limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{2},HA_{1}})}}&{\sum% \limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{2},HA_{2}})}}&\ldots&{\sum\limits_{j=% 1}^{n}{\textit{PLDD}_{j}({HA_{2},HA_{m}})}}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ {HA_{m}}&{\sum\limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{m},HA_{1}})}}&{\sum% \limits_{j=1}^{n}{\textit{PLDD}_{j}({HA_{m},HA_{2}})}}&\ldots&{\sum\limits_{j=% 1}^{n}{\textit{PLDD}_{j}({HA_{m},HA_{m}})}}\\ \end{array}}}\right]$

(4) Finally, the probabilistic linguistic overall dominance degree $\textit{PLODD}({HA_{i}})$ of alternative $HA_{i}$ is obtained:

$\displaystyle\textit{PLODD}({HA_{i}})=\frac{\sum\limits_{t=1}^{m}{\textit{PLDD% }_{it}-\mathop{\min}\limits_{i}\left\{{\sum\limits_{t=1}^{m}{\textit{PLDD}_{it% }}}\right\}}}{\mathop{\max}\limits_{i}\left\{{\sum\limits_{t=1}^{m}{\textit{% PLDD}_{it}}}\right\}-\mathop{\min}\limits_{i}\left\{{\sum\limits_{t=1}^{m}{% \textit{PLDD}_{it}}}\right\}},i=1,2,\ldots,m.$ (13)

(5) The order could be sorted according to $\textit{PLODD}({HA_{i}})({i=1,2,\ldots,m})$ , that is, the greater $\textit{PLODD}({HA_{i}})({i=1,2,\ldots,m})$ , the better the alternative $HA_{i}$ is.

4. An empirical example and comparative analysis

4.1 An empirical example

Information management is a discipline that uses information technology as a means to study the distribution, composition, collection, processing, exchange, development, utilization, and service of information. The complex information can only be effectively processed before it can be used, while the already organized information resources can only be maintained in an orderly manner through strengthened management, in order to achieve optimal development and utilization, and to unleash their application value. There are currently many research achievements and mature systems in network operation management, and the OSI network management model refers to this type of network management. Network information management is the management of network information and its services, with the goal of ensuring services and applications. It comprehensively integrates and manages information resource organization, information platform coordination, user permission management, and security prevention strategies. It manages resources such as network applications, network services, network information, security, and users. The correct handling of network information and effective management of information services are the foundation for promoting network development and effectively utilizing network resources. The rapid development of the internet has greatly promoted social development and economic leap. For an already networked society and enterprises, normal network operation and information services are extremely important. However, there are always some insecure factors in the network that pose a great threat to computer network information, especially for Internet Content Provider (ICP) and Application Service Provider (ASP). Therefore, the security, ease of operation, and A series of issues such as ease of management. Information security is a comprehensive topic that involves legislation, technology, management, usage, and many other aspects. These have put forward higher requirements for network information security protection, and also make the position of the subject of network information security increasingly important. Network information security will inevitably continue to develop with the development of network applications. The computer network security evaluation is a classical MAGDM issue. Therefore, the computer network security evaluation is presented to demonstrate the approach developed in this paper. There is a panel with five computer network systems $HA_{i}({i=1,2,3,4,5})$ to choose. The experts select four attributes to assess the five primary and secondary schools: ⟀ HG ${}_{1}$ is the entity and environment security of the network; ⟁ HG ${}_{2}$ is the organization and management of the network; ⟂ HG ${}_{3}$ is the safe practice measures; ⟃ HG ${}_{4}$ is the communication security of the network. The five potential computer network systems $HA_{i}({i=1,2,3,4,5})$ are to be assessed by utilizing the linguistic term set $H L$ by five invited experts.

$\displaystyle HL=\{hl_{-3}=\textit{extremely poor}(\textit{HEP}),hl_{-2}=% \textit{very poor}(\textit{HVP}),$ $\displaystyle hl_{-1}=\textit{poor}(HP),hl_{0}=\textit{medium}(HM),hl_{1}=% \textit{good}(HG),$ $\displaystyle hl_{2}=\textit{very good}(\textit{HVG}),hl_{3}=\textit{extremely% good}(HEG)\}$

Then, the probabilistic linguistic information is obtained through performing statistical processing on the group linguistic evaluation information of five experts. the probabilistic linguistic information is listed in the Table 1.

Table 1
PL-matrix

Alternatives	HG ${}_{1}$
HA ${}_{1}$	$\{{hl_{-2}(0.1),hl_{-1}(0.7),hl_{0}(0.1),hl_{2}({0.1})}\}$
HA ${}_{2}$	$\{{hl_{0}(0.3),hl_{1}(0.4),hl_{2}({0.3})}\}$
HA ${}_{3}$	$\{{hl_{0}(0.4),hl_{1}(0.2),hl_{2}(0.2),hl_{3}({0.2})}\}$
HA ${}_{4}$	$\{{hl_{-2}(0.4),hl_{1}(0.5),hl_{2}({0.1})}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.6),hl_{1}(0.2),hl_{2}({0.2})}\}$
Alternatives	HG ${}_{2}$
HA ${}_{1}$	$\{{hl_{-1}({0.2}),hl_{-2}({0.1}),hl_{1}({0.1}),hl_{2}(0.3),hl_{3}(0.3)}\}$
HA ${}_{2}$	$\{{hl_{-1}(0.8),hl_{1}(0.1),hl_{2}(0.1)}\}$
HA ${}_{3}$	$\{{hl_{-2}({0.4}),hl_{-1}(0.1),hl_{2}(0.5)}\}$
HA ${}_{4}$	$\{{hl_{-2}({0.2}),hl_{0}(0.4),hl_{1}(0.1),hl_{2}(0.3)}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.9),hl_{1}(0.1)}\}$
Alternatives	HG ${}_{3}$
HA ${}_{1}$	$\{{hl_{1}(0.4),hl_{2}(0.4),hl_{3}({0.2})}\}$
HA ${}_{2}$	$\{{hl_{-1}(0.3),hl_{1}(0.2),hl_{2}({0.5})}\}$
HA ${}_{3}$	$\{{hl_{0}(0.4),hl_{1}(0.6)}\}$
HA ${}_{4}$	$\{{hl_{-1}(0.2),hl_{0}(0.3),hl_{1}({0.5})}\}$
HA ${}_{5}$	$\{{hl_{1}(0.6),hl_{2}(0.4)}\}$
Alternatives	HG ${}_{4}$
HA ${}_{1}$	$\{{hl_{-1}(0.7),hl_{1}(0.2),hl_{2}(0.1)}\}$
HA ${}_{2}$	$\{{hl_{-2}({0.4}),hl_{-1}(0.1),hl_{1}(0.3),hl_{3}(0.2)}\}$
HA ${}_{3}$	$\{{hl_{-3}({0.2}),hl_{-2}({0.1}),hl_{-1}(0.2),hl_{2}(0.5)}\}$
HA ${}_{4}$	$\{{hl_{0}({0.6}),hl_{1}(0.1),hl_{3}(0.3)}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.2),hl_{1}(0.8)}\}$

Then, the PL-ExpTODIM method is designed for computer network security evaluation.

Step 1. Obtain the normalized PL-matrix (Table 2).

Table 2

Normalized PL-matrix

Alternatives	HG ${}_{1}$
HA ${}_{1}$	$\{{hl_{-2}(0.0),hl_{-2}(0.1),hl_{-1}(0.7),hl_{0}(0.1),hl_{2}({0.1})}\}$
HA ${}_{2}$	$\{{hl_{0}(0.0),hl_{0}(0.0),hl_{0}(0.3),hl_{1}(0.4),hl_{2}({0.3})}\}$
HA ${}_{3}$	$\{{hl_{0}(0.0),hl_{0}(0.4),hl_{1}(0.2),hl_{2}(0.2),hl_{3}({0.2})}\}$
HA ${}_{4}$	$\{{hl_{-2}(0.0),hl_{-2}(0.0),hl_{-2}(0.4),hl_{1}(0.5),hl_{2}({0.1})}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.6),hl_{1}(0.2),hl_{2}({0.2})}\}$
Alternatives	HG ${}_{2}$
HA ${}_{1}$	$\{{hl_{-1}({0.2}),hl_{-2}({0.1}),hl_{1}({0.1}),hl_{2}(0.3),hl_{3}(0.3)}\}$
HA ${}_{2}$	$\{{hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.8),hl_{1}(0.1),hl_{2}(0.1)}\}$
HA ${}_{3}$	$\{{hl_{-2}({0.0}),hl_{-2}({0.0}),hl_{-2}({0.4}),hl_{-1}(0.1),hl_{2}(0.5)}\}$
HA ${}_{4}$	$\{{hl_{-2}({0.0}),hl_{-2}({0.2}),hl_{0}(0.4),hl_{1}(0.1),hl_{2}(0.3)}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.9),hl_{1}(0.1)}\}$
Alternatives	HG ${}_{3}$
HA ${}_{1}$	$\{{hl_{1}(0.4),hl_{2}(0.4),hl_{3}({0.2})}\}$
HA ${}_{2}$	$\{{hl_{-1}(0.3),hl_{1}(0.2),hl_{2}({0.5})}\}$
HA ${}_{3}$	$\{{hl_{0}(0.4),hl_{1}(0.6)}\}$
HA ${}_{4}$	$\{{hl_{-1}(0.2),hl_{0}(0.3),hl_{1}({0.5})}\}$
HA ${}_{5}$	$\{{hl_{1}(0.6),hl_{2}(0.4)}\}$
Alternatives	HG ${}_{4}$
HA ${}_{1}$	$\{{hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.7),hl_{1}(0.2),hl_{2}(0.1)}\}$
HA ${}_{2}$	$\{{hl_{-2}({0.0}),hl_{-2}({0.4}),hl_{-1}(0.1),hl_{1}(0.3),hl_{3}(0.2)}\}$
HA ${}_{3}$	$\{{hl_{-3}({0.0}),hl_{-3}({0.2}),hl_{-2}({0.1}),hl_{-1}(0.2),hl_{2}(0.5)}\}$
HA ${}_{4}$	$\{{hl_{0}({0.0}),hl_{0}({0.0}),hl_{0}({0.6}),hl_{1}(0.1),hl_{3}(0.3)}\}$
HA ${}_{5}$	$\{{hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.0),hl_{-1}(0.2),hl_{1}(0.8)}\}$

Step 2. Obtain the weight values.

Table 3

The attributes weight

	HG ${}_{1}$	HG ${}_{2}$	HG ${}_{3}$	HG ${}_{4}$
$h w$	0.1462	0.3483	0.3049	0.2006

Step 3. Obtain the relative weight.

Table 4

The relative attributes weight

	HG ${}_{1}$	HG ${}_{2}$	HG ${}_{3}$	HG ${}_{4}$
rhw	0.4198	1.0000	0.8754	0.5759

Step 4. Obtain the overall PLDD matrix (See Table 5).

Table 5

The overall PLDD matrix $\textit{PLDD}=({\textit{PLDD}_{ij}})_{5\times 4}$

Alternatives	HA ${}_{1}$	HA ${}_{2}$	HA ${}_{3}$	HA ${}_{4}$	HA ${}_{5}$
HA ${}_{1}$	0.0000	$-$ 1.2895	0.9786	$-$ 1.5032	0.7217
HA ${}_{2}$	$-$ 0.1546	0.0000	0.9476	0.1202	$-$ 1.5135
HA ${}_{3}$	1.1275	$-$ 1.7217	0.0000	$-$ 1.8477	1.0468
HA ${}_{4}$	$-$ 0.5095	$-$ 0.7117	1.1557	0.0000	$-$ 0.4882
HA ${}_{5}$	0.9932	$-$ 1.8233	$-$ 0.0730	$-$ 1.6863	0.0000

Step 5. Calculate the $\textit{PLODD}({HA_{i}})({i=1,2,\ldots,5})$ (Table 6).

Table 6

The $\textit{PLODD}({HA_{i}})$

Alternatives	HA ${}_{1}$	HA ${}_{2}$	HA ${}_{3}$	HA ${}_{4}$	HA ${}_{5}$
PLODD	0.7465	0.9884	0.5978	1.0000	0.0000

Step 8. Finally, the order could be obtained: $HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$ , and thus the optimal computer network systems is $HA_{4}$ .

4.2 Comparative analysis

Then, the PL-ExpTODIM method is compared with PL-ELECTRE II method [49], PL-MULTIMOORA method [50], PL-CODAS [51], PL-ORESTE method [52] and PL-WASPAS method [48]. The comparative decision results are shown in Table 7.

Table 7
Order of the different methods

	Ordering
PLWA operator [45]	$HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$
PL-MULTIMOORA method [50]	$HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$
PL-CODAS method [51]	$HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$
PL-ORESTE method [52]	$HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$
PL-WASPAS method [48]	$HA_{4}\succ HA_{2}\succ HA_{1}\succ HA_{3}\succ HA_{5}$

In the light with WS coefficients [53, 54], the WS coefficient between the PL-ELECTRE II method [49], PL-MULTIMOORA method [50], PL-CODAS [51], PL-ORESTE method [52], PL-WASPAS method [48] and the proposed PL-ExpTODIM method is 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, respectively. From the above detailed analysis, it could be seen that these six methods have the same optimal computer network systems and worst computer network systems. Furthermore, the order of these six methods is same. This verifies the PL-ExpTODIM method is effective.

5. Conclusion

The functions of modern computer systems are becoming increasingly complex, and the network system is becoming increasingly powerful, which is having a huge and profound impact on society. However, at the same time, due to the diversity of connection forms, uneven distribution of terminals, and the openness and interconnection of networks, computer network security is facing threats, such as entity destruction, unintentional errors, vulnerabilities in network software, and “backdoor” attacks, so it makes security issues increasingly prominent. Therefore, it is necessary to improve the defense capability of computer networks and strengthen network security measures, otherwise the network will be useless and even endanger national security. Whether in a local area network or a wide area network, there are vulnerabilities and potential threats from natural and human factors. Therefore, the defense measures of the network should be able to comprehensively address various threats and vulnerabilities, in order to ensure the confidentiality, integrity, and availability of network information. The computer network security evaluation is classical MAGDM. Recently, the ExpTODIM method has been used to cope with MAGDM issues. The PLTSs are used as a tool for characterizing uncertain information during the quality evaluation of continuing education for computer network security evaluation. In this manuscript, the probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is built to solve the MAGDM under PLTSs. In the end, a numerical case study for computer network security evaluation is given to validate the proposed method. In our future works, the designed methods under PLTSs needs to be discussed under probabilistic uncertain linguistic setting and uncertain probabilistic linguistic setting [55, 56, 57, 58, 59, 60, 61, 62].

References

Abraham

Smith

Jain

. Network and information security: A computational intelligence approach Special Issue of Journal of Network and Computer Applications. J Netw Comput Appl. 2007; 30(1): 1-3.

Adams

. Network security: It’s not just about computers anymore. Commun News. 2000; 37(6): 32.

Anagun

. Development of committee neural network for computer access security system. In: Gavrilova M, Gervasi O, Kumar V, Tan CJK, Taniar D, Lagana A, et al., editors. Computational Science and Its Applications – Iccsa 2006, Pt 3. Lecture Notes in Computer Science. 3982. Berlin: Springer-Verlag Berlin; 2006. pp. 11-20.

Cervone

. Computer network security and cyber ethics. Portal-Libr Acad. 2007; 7(2): 249-50.

Eng

. Computer network security for the radiology enterprise. Radiology. 2001; 220(2): 303-9.

Wang

Sharma

Singh

Gaba

Masud

, et al. An exhaustive research on the application of intrusion detection technology in computer network security in sensor networks. J Sens. 2021; 2021: 11.

Thuraisingham

Xiang

. Special issue on frontiers of trust, security and privacy for computer and communication networks. J Internet Technol. 2014; 15(3): 451-2.

. Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators. J Intell Fuzzy Syst. 2020; 39(3): 4427-41.

Zhao

Masood

Seneviratne

. A review of computer vision methods in network security. IEEE Commun Surv Tutor. 2021; 23(3): 1838-78.

10.

Zheng

. Analysis of application strategies of computer information management technology in maintaining network security. Basic Clin Pharmacol Toxicol. 2019; 125: 225.

11.

Zou

. Optimization strategy of computer network information security from the perspective of cognitive impairment. Psychiatr Danub. 2022; 34: S286-S7.

12.

Zhang

. Research on the computer network security evaluation based on the DHFHCG operator with dual hesitant fuzzy information. J Intell Fuzzy Syst. 2015; 28(1): 199-204.

13.

Zhang

Xiao

Chen

Zhang

Deng

. A survey of security visualization for computer network logs. Secur Commun Netw. 2012; 5(4): 404-21.

14.

Zhao

Wang

. An analysis of internet of things computer network security and remote control technology. Wirel Commun Mob Comput. 2022; 2022: 13.

15.

Sasaki

Watanabe

Sakabe

. Computer network system with security for a protein data collection system at the Photon Factory. J Synchrot Radiat. 1999; 6: 116-8.

16.

Schechter

Smith

. How much security is enough to stop a thief? The economics of outsider theft via computer systems and networks. In: Wright RN, editor. Financial Cryptography, Proceedings. Lecture Notes in Computer Science. 2742. Berlin: Springer-Verlag Berlin; 2003. pp. 122-37.

17.

Shandilya

Upadhyay

Kumar

Nagar

. AI-assisted Computer Network Operations testbed for Nature-Inspired Cyber Security based adaptive defense simulation and analysis. Futur Gener Comp Syst. 2022; 127: 297-308.

18.

Liu

. Computer network confidential information security based on big data clustering algorithm. Wirel Commun Mob Comput. 2022; 2022: 10.

19.

. The construction method of computer network security defense system based on multisource big data. Sci Program. 2022; 2022: 13.

20.

Mohammadi

Sherkat

Jamporazmey

. A taxonomy framework based on ITU-TX-805 security architecture for quantitative determination of computer network vulnerabilities. Secur Commun Netw. 2013; 6(7): 864-80.

21.

Kraemer

Carayon

. Human errors and violations in computer and information security: The viewpoint of network administrators and security specialists. Appl Ergon. 2007; 38(2): 143-54.

22.

. Application of data image encryption technology in computer network information security. Math Probl Eng. 2022; 2022: 7.

23.

Lin

Yang

Chen

. The application of computer intelligence in the cyber-physical business system integration in network security. Comput Intell Neurosci. 2022; 2022: 10.

24.

Linkov

Varghese

Jamil

Seager

Kiker

Bridges

, editors. Multi-criteria decision analysis: A framework for structuring remedial decisions at contaminated sites. NATO Advanced Research Workshop on Comparative Risk Assessment and Environmental Decision Making; 2002 Oct 13–16; Rome, ITALY. DORDRECHT: Springer; 2004.

25.

Pusic

Lusic

. Multi-criteria decision analysis for nautical anchorage selection. Journal of Marine Science and Engineering. 2023; 11(4): 21.

26.

Saha

Villuri

VGK

Bhardwaj

Kumar

. A Multi-Criteria Decision Analysis (MCDA) Approach for Landslide Susceptibility Mapping of a Part of Darjeeling District in North-East Himalaya, India. Applied Sciences-Basel. 2023; 13(8): 23.

27.

Wieckowski

Watrobski

Kizielewicz

Salabun

. Complex sensitivity analysis in Multi-Criteria Decision Analysis: An application to the selection of an electric car. Journal of Cleaner Production. 2023; 390: 15.

28.

Wilkins

Rychert

Queirolo

Lenton

Kilmer

Fischer

, et al. Assessing options for cannabis law reform: A Multi-Criteria Decision Analysis (MCDA) with stakeholders in New Zealand. Int J Drug Policy. 2022; 105: 10.

29.

Bhuyan

Deka

Saikia

. Micro-spatial flood risk assessment in Nagaon district, Assam (India) using GIS-based multi-criteria decision analysis (MCDA) and analytical hierarchy process (AHP). Risk Analysis. 2023; 16.

30.

Iweh

Semassou

Ahouansou

. Optimum Site Selection of Hybrid Solar Photovoltaic (PV)-Hydro Power Plants in off Grid Locations in Cameroon using the Multi-Criteria Decision Analysis (MCDA). Energy Sources Part a-Recovery Utilization and Environmental Effects. 2023; 45(3): 8076-91.

31.

Munier

. A new approach to the rank reversal phenomenon in MCDM with the SIMUS method. Multiple Criteria Decision Making. 2016; (11): 137-52.

32.

Stoilova

. An integrated multi-criteria approach for planning railway passenger transport in the case of uncertainty. Symmetry [Internet]. 2020; 12(6).

33.

Stoilova

Munier

Kendra

Skrúcaný

. Multi-Criteria Evaluation of Railway Network Performance in Countries of the TEN-T Orient-East Med Corridor. Sustainability. 2020; 12(4): 1482.

34.

Stoilova

Munier

. A novel fuzzy SIMUS multicriteria decision-making method. An application in railway passenger transport planning. Symmetry [Internet]. 2021; 13(3): 483.

35.

Wieckowski

Kizielewicz

Shekhovtsov

Salabun

. RANCOM: A novel approach to identifying criteria relevance based on inaccuracy expert judgments. Engineering Applications of Artificial Intelligence. 2023; 122: 21.

36.

Stanujkic

Karabasevic

Zavadskas

Smarandache

Brauers

WKM

. A bipolar fuzzy extension of the MULTIMOORA method. Informatica. 2019; 30(1): 135-52.

37.

Roy

Sharma

Kar

Zavadskas

Saparauskas

. An extended COPRAS model for multi-criteria decision-making problems and its application in web-based hotel evaluation and selection. Economic Research-Ekonomska Istrazivanja. 2019; 32(1): 219-53.

38.

Liu

Chen

. Group decision making based on heronian aggregation operators of intuitionistic fuzzy numbers. Ieee Transactions on Cybernetics. 2017; 47(9): 2514-30.

39.

Fei

. A compromise-typed variable weight decision method for hybrid multiattribute decision making. Ieee Transactions on Fuzzy Systems. 2019; 27(5): 861-72.

40.

Ren

Gou

. Pythagorean fuzzy TODIM approach to multi-criteria decision making. Applied Soft Computing. 2016; 42: 246-59.

41.

Tversky

Kahneman

. Prospect theory: An analysis of decision under risk. Econometrica. 1979; 47(2): 263-91.

42.

Gomes

Lima

. TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Foundations of Computing and Decision Sciences. 1979; 16: 113-27.

43.

Leoneti

Gomes

. A novel version of the TODIM method based on the exponential model of prospect theory: The ExpTODIM method. European Journal of Operational Research. 2021; 295(3): 1042-55.

44.

Sun

Yang

Cai

Wei

. An extended Exp-TODIM method for multiple attribute decision making based on the Z-Wasserstein distance. Expert Systems with Applications. 2023; 214: 14.

45.

Pang

Wang

. Probabilistic linguistic linguistic term sets in multi-attribute group decision making. Information Sciences. 2016; 369: 128-43.

46.

M.W.

, X

Z.S.

,Probabilistic Linguistic Distance Measures and Their Applications in Multi-criteria Group Decision Making, In: Collan M, Kacprzyk J (eds) Soft Computing Applications for Group Decision-making and Consensus Modeling Studies in Fuzziness and Soft Computing Springer, Cham. 2018; 357.

47.

Shannon

. A mathematical theory of communication. Bell System Technical Journal. 1948; 27(4): 379-423.

48.

Darko

Liang

. Probabilistic linguistic WASPAS method for patients’ prioritization by developing prioritized Maclaurin symmetric mean aggregation operators. Applied Intelligence. 2022; 52(8): 9537-55.

49.

Pan

Ren

. Therapeutic Schedule Evaluation for Brain-Metastasized Non-Small Cell Lung Cancer with A Probabilistic Linguistic ELECTRE II Method. International Journal of Environmental Research and Public Health. 2018; 15(9): 23.

50.

Zhao

Wang

Feng

Zhou

Lev

. Integrated BWM-Entropy weighting and MULTIMOORA method with probabilistic linguistic information for the evaluation of Waste Recycling Apps. Applied Intelligence. 2023; 53(1): 813-36.

51.

Chen

Gou

. The application of probabilistic linguistic CODAS method based on new score function in multi-criteria decision-making. Computational & Applied Mathematics. 2022; 41(1): 25.

52.

Liu

Wang

. The probabilistic linguistic term sets based ORESTE method for risk evaluation in Fine-Kinney model with interactive risk factors. Journal of Intelligent & Fuzzy Systems. 2022; 43(3): 3493-512.

53.

Salabun

Urbaniak

, editors. A New Coefficient of Rankings Similarity in Decision-Making Problems. 20th Annual International Conference on Computational Science (ICCS); 2020 Jun 03–05; Amsterdam, NETHERLANDS. CHAM: Springer International Publishing Ag; 2020.

54.

Sałabun

Wa̧tróbski

Shekhovtsov

. Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods. Symmetry. 2020; 12(9): 1549.

55.

Lin

Zhai

Yao

. Multi-attribute group decision-making under probabilistic uncertain linguistic environment. Journal of the Operational Research Society. 2018; 69(2): 157-70.

56.

Gong

Chen

. A programming-based algorithm for probabilistic uncertain linguistic intuitionistic fuzzy group decision-making. Symmetry-Basel. 2019; 11(2).

57.

Xie

Ren

Wang

. The consensus of probabilistic uncertain linguistic preference relations and the application on the virtual reality industry. Knowledge-Based Systems. 2018; 162: 14-28.

58.

Wei

Lei

Wei

Guo

. Green supplier selection with an uncertain probabilistic linguistic MABAC method. Journal of Intelligent & Fuzzy Systems. 2020; 39(3): 3125-36.

59.

Zhao

Gao

Wei

Guo

. Model for network security service provider selection with probabilistic uncertain linguistic TODIM method based on prospect theory. Technological and Economic Development of Economy. 2022; 28(3): 638-54.

60.

Zhang

. Comparison and operators based on uncertain probabilistic linguistic term set. Journal of Intelligent & Fuzzy Systems. 2019; 36(6): 6359-79.

61.

Zhao

Wei

Chen

. Probabilistic Uncertain Linguistic EDAS Method Based on Prospect Theory for Multiple Attribute Group Decision-Making and Its Application to Green Finance. International Journal of Fuzzy Systems. 2022; 24(3): 1318-31.

62.

Jin

Wang

. Uncertain probabilistic linguistic term sets in group decision making. International Journal of Fuzzy Systems. 2019; 21(4): 1241-58.

A fuzzy group decision-making framework for computer network security evaluation with probabilistic linguistic information

Abstract

Keywords

1. Introduction

2. Preliminaries

3.1 Construct the probabilistic linguistic information

3.2 Obtain the attributes weight with information entropy

4.1 An empirical example

Table 1 PL-matrix

Table 7 Order of the different methods

References

Table 1
PL-matrix

Table 7
Order of the different methods