Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations

Abstract

Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using it. Despite the many benefits of technology, several risks and serious threats, called cyberattacks, are associated with it. The method of neutralizing these cyberattacks is known as cybersecurity. Sometimes, there are uncertainties in recognizing a cyberattack and nullifying its effects using righteous cybersecurity. For that reason, this article introduces interval-valued complex intuitionistic fuzzy relations (IVCIFRs). For the first time in the theory of fuzzy sets, we investigated the relationships among different types of cybersecurity and the sources of cyberattacks. Moreover, the Hasse diagram for the interval-valued complex intuitionistic partial order set and relation is defined. The concepts of the Hasse diagram are used to inspect different cybersecurity techniques and practices. Then, using the properties of Hasse diagrams, the most beneficial technique is identified. Furthermore, the best possible selection of types of cybersecurity is made after putting some restrictions on the selection. Lastly, the advantages of the proposed methods are illuminated through comparison tests.

[Retracted] Analysis of Communication and Network Securities Using the Concepts of Complex Picture Fuzzy Relations

“…Yazdanbakhsh and Dick [ 26 ] reviewed the CFSs, Dick [ 27 ] studied the complex fuzzy logic, Nasir et al [ 28 – 31 ] proposed rich applications of complex fuzzy relations and its generalizations, Thirunavukarasu et al [ 32 ] proposed the applications of CFSs, Ngan et al [ 33 ] applied and represented the CIFS by quaternion numbers, Alkouri and Salleh [ 34 ] worked on complex IFRs (CIFRs), and Yaqoob et al [ 35 ] applied the CIFRs to cellular network provide companies. Jan et al [ 36 , 37 ] initiated the innovative concepts of CIFRs and IVCIFRs and proposed the applications of said concepts in the analysis of cyber-securities, cyber threats in petroleum sectors, and other industries. Lin et al [ 38 – 40 ] worked comprehensively on decision-making techniques in the environment of picture fuzzy information.…”

An Innovative Decision-Making Approach Based on Correlation Coefficients of Complex Picture Fuzzy Sets and Their Applications in Cluster Analysis

“…13. Let Y � y, ξ(y)e ρ ξ (y)2πi , α(y)e ρ α (y)2πi , 􏼈 η(y)e ρ η (y)2πi : y ∈ R} and Z � z, ξ(z)e ρ ξ (z)2πi , α(z)e ρ α (z)2πi , 􏼈 η(z)e ρ η (z)2πi : z ∈ R} be any CPFSs on a referential set R, then their correlation coefficient denoted by ∁' is also calculated by formula (18) or alternatively formula (19):…”

“…Yaqoob et al [16] used CIFSs in cellular network providers' corporations. Nasir et al [17][18][19] applied the CFSs, complex fuzzy relations (CFRs), and their generalizations to cybersecurity and network security. References [20][21][22] majorly worked on DM methods under the complex fuzzy information.…”

A Novel Approach to Model the Economic Characteristics of an Organization by Interval-Valued Complex Pythagorean Fuzzy Information

“…F A S Zhang [28] presented the origination of interval valued intuitionistic fuzzy relation (IVIFR). A Nasir et al [29] proposed the interval valued complex intuitionistic fuzzy relation (IVCIFR). According of FSs, that defines the only membership but can also covers the non-membership in [0,1].…”