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

Abstract

In our lives, we cannot avoid the uncertainty. Randomness, rough knowledge, and vagueness lead us to uncertainty. In mathematics, the fuzzy set (FS) theory and logics are used to model uncertain events. This article defines a new concept of complex picture fuzzy relation (CPFR) in the field of FS theory. In addition, the types of CPFRs are also discussed to make the paper more fruitful. Today’s complex network architecture faces the ever-changing threats. The cyber-attackers are always trying to discover, catch, and exploit the weaknesses in the networks. So, the security measures are essential to avoid and dismantle such threats. The CPFR has a vast structure composed of levels of membership, abstinence, and nonmembership which models uncertainty better than any other structures in the theory. Moreover, a CPFR has the ability to cope with multivariable problems. Therefore, this article proposes modeling techniques based on the complex picture fuzzy information which are used to study the effectiveness and ineffectiveness of different network securities against several threats and cyber-attack practices. Moreover, the strength and preeminence of the proposed methods are verified by studying their comparison with the existing methods.

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 new approach to investigate the effects of artificial neural networks based on bipolar complex spherical fuzzy information

“…CPFS defines three stages of an element with both amplitude term (AT) and phase term (PT). Nasir et al [33] introduced the complex picture FR (CPFR) using the Cartesian product (CP) of two CPFS with the application of network security. Mahmood et al [34] established the concept of spherical fuzzy set (SFS) with the application of decision-making and medical diagnosis problems.…”

Analysis of Risks and Security of E-Commerce by Using the Novel Concepts of Complex Cubic Picture Fuzzy Information

“…All the three stages represent in form of complex number and sum of right extremes of interval and sum of left extremes of interval ranging between [0,1]. Nasir et al [29] proposed an application of CoPFRs in communication and network security.…”