One of the main Cyber security's task is to ensure the real time protection of information and networks. In the last decade the number of cyber security attacks and its frequency has increased, creating the need for new data protection systems. In this paper we present two groups of criteria with a total of eight sub-criteria afecting cyber security, and their ranking using Fuzzy AHP. The Data/password leak, Fishing detection and DoS attack detection are recognized as the most important sub-criteria.
The information is always considered as an important Let all fuzzy sets defined on the set of real numbers R be part in the sustainable success competitivness. The rapid represented as (R). The number ∈ (R) is a fuzzy development of IoT, cloud computing and data transfer, number if there exists 0 ∈ R so condition (0) = 1 influencing the thinking of people and changing their holds, and = [︀ , () ≥ ]︀ is a closed interval lifestyle increase the number of exploitable vulnerabili- for every ∈ [0, 1] [1]. The membership function, a ties. To ensure real-time protection of information and component of a triangular fuzzy number (TFN) , is a information systems from intruders, organizations spent function : R → [0, 1], defined as a lot of efort and resources in determining the intrusbiroenacchrietseroivaedrettheremlainstattwioon.dTehcaedneusmisbceornosftcaynbtleyrsienccureriatsy- () = ⎨⎧ ((− − ))//((− − )),, ≤ ≤ ≤ ≤ ,, ing, and diferent approaches and techniques have been ⎩ 0, otherwise, introduced by researchers and experts to implement robust security mechanisms. Defining and ranking of criteria afecting intrusion systems become challenging issue for researchers and cyber security experts often applying some of the MCDM approaches.
= (1 − 2, 1 − 2, 1 − 2), ˜ ˜ 1 ⊗ 2 = (1, 1, 1) ⊗ (2, 2, 2)
= (1 · 2, 1 · 2, 1 · 2), · ˜1 = · (1, 1, 1) = ( · 1, · 1, · 1), ˜−1 1 = (1, 1, 1)− 1 = (1/1,1/1,1/1). given as
For a given triangular number ˜ = (, , ) the left side of the membership function ˜ and it’s inverse are ˜ = ( − )/( − ); ( ˜)− 1
= + ( − ), ∈ [0, 1], it’s inverse are given as and the right side of the membership function ˜ and ˜ = ( − )/( − ); ( ˜)− 1 = + ( − ), ∈ [0, 1].
∫︁ 1 0
( ˜)− 1 is (˜) = (˜) + (1 − )(˜) = = 1 2 ∫︁ 1 0
( ˜)− 1 + (1 − ) ( + + (1 − )) .
where represents an optimism index. The optimistic ( = 1), balanced ( = 0.5) and pessimistic (
= 0) point of view are significant to obtain and rank criteria, while semi-pessimistic (
= 0.25) and semi-optimistic (
= 0.75) point of view are used when additional opinion is needed or more accurate results required [5].
Since its creation [6], the Analytic Hierarchy Process
(AHP) had a respectable application in MCDM, enabling
the decision makers to solve complex problems by
decomposing them into a hierarchical structure, creating the
comparison matrix and determining the importance of
one indicator above others. The specified level of
uncertainty of a team of experts (or even one expert) [7] due to
the inability to express the significance of some criteria
has led to the introduction of Fuzzy AHP [8, 9] enabling
0
2
4
6
8
10
12
(
The total integral value, according to [4] as a combination of left and right integral values (˜) and (˜), of TFNs. In this step, a positive fuzzy reciprocal comparexpressions. Determining the pairwise comparison matrix ̃︀ in terms conversion of linguistic statements into mathematical should be found and calculations repeated [14].
The phases in FAHP can be summarized as follows
Using the triangular fuzzy numbers from the comparison
(
As it was recommended in [11], a fuzzy distance of 2 and odd values as boundaries for all non-intermediate values are applied in order to achieve better consistency.
There are also diferent scales of triangular fuzzy numbers applicable in the previous case [12, 13].
The graphic representation of the used FAHP scale with all three values (lower, median, and upper) is presented in Figure 1.
Phase III: Matrix consistency review For a matrix = ( )× , the consistency index and consistency ratio are calculated using equations −
− 1 = , = ,
(5) where max corresponds to a maximal eigenvalue of matrices and is a random index, as shown in Table 2. The values for matrices of dimensions of one and two are equal to zero.
The value < 0.1 confirms the comparison matrix consistency, while otherwise the reason for inconsistency
Phase IV: The fuzzification phase matrix ̃︀ = (︀ ˜ × ︀)
, applying and
TFNs
(
Inverse TFNs (1/3, 1, 1) (1/3, 1/2, 1) (1/5, 1/3, 1) (1/5, 1/4, 1/3) (1/7, 1/5, 1/3) (1/7, 1/6, 1/5) (1/9, 1/7, 1/5) (1/9, 1/8, 1/7) (1/9, 1/9, 1/7)
0.58
0.90
1.12 Six 1.24
1.32
1.41
1.45
Ten 1.49 the value of the fuzzy synthetic extent is obtained as
3. Literature preview and Cyber − 1 = ︃( ∑︁ ∑︁ ˜ ̃︀ = ∑︁ ˜
⊗ − 1 =1 =1 = ∑︁ ( , , ) ⊗ − 1, = 1, .
Phase V: The defuzzification phase The defuzzification phase starts with the weighted vector in order to obtain the total integral value for the TFNs, ̃︀ [15] 1 2 = (̃︀) =
︀( + + (1 − ))︀ , ∈ [0, 1], = 1, , Phase VI: Normalization phase criteria are obtained.
* = ∑︀ =1 (10) (7) (8) (9)
Phase VII: Ranking phase The weights for each sub-criterion are obtained by multiplying the weights of the criteria and sub-criteria. Then, arranging the obtained weights, the sub-criteria ranking is received.
security criteria In this section the literature preview of security indicators followed by selected criteria will be given.
The internet changed the concept of computing as we know it, enlarging the number of possibilities and opportunities, which lead to the higher number of risks, possible vulnerabilities and system breakthroughs. Computer security primarily focuses on protecting a specific source or valuable data and information within a single computer device. Security is defined as the reaction taken to security threats resulting from a harmful act by some people [16]. AHP and its various generalizations (MCDM approaches) ofer a lot of potential in the process of solving hierarchical decision-making problems.
Since Saaty proposed it, AHP method was used to calcuIn the normalization phase, the weight vectors * for late the weights of criteria significantly advancing this 3˜− 1 4˜− 1 5˜− 1 X21 2˜− 1 3˜− 1 5˜− 1 2˜− 1 4˜− 1 2˜− 1 4˜− 1 3˜− 1 2˜− 1 process in finding the decision that best matches given conditions. Some of the recent publications regarding security criteria are published by Almotiri [17] exploring the efectiveness of malicious trafic detention systems, Goutam et al [18] established techniques for identifying shortcoming of online applications, Agarwal et al tested university’s software security using ANP-TOPSIS evaluation [19]. The AHP-TOPSIS based approach dealed with healthcare electronic service quality making the interactivity, service correctness, and responsiveness the most important characteristics in providing satisfying and effective healthcare web services was presented in [20], while in [21] using the same methodology under hesitant fuzzy conditions Sahu presented a novel framework for software durability assessment. Alharbe [22] also used MCDM approaches in recognizing and prioritizing usable security attributes while designing and developing the software, and in [23] authors determined and prioritized confidence parameters in fog computing.
In the sequel we present criteria and sub-criteria related to cyber secutity.
Applying the AHP and the FAHP method presented in previous section, ranking of main criteria is ob- attacks, which corresponds to results presented in [24]. tained.
The pairwise comparison matrix for main criteria is consistent since =
Obtained weights (1) =
0.666666667 and (2) 0.333333333 in the case of AHP and (1) = =
The highest ranked sub-criteria in PDM group is approximately 7.39 times higher than lowest ranked sub-criteria in the AHP case, and 6.77 higher in the balanced FAHP case.