Evaluation of the Economic Relationships on the Basis of Statistical Decision-Making in Complex Neutrosophic Environment

Abstract

Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations (CNRs) and its types based on the idea of complex neutrosophic sets (CNSs). In addition, these concepts are supported by suitable examples. A CNR discusses the quality of a relationship using the degree of membership, the degree of abstinence, and the degree of nonmembership. Each of these degrees is a complex number from the unit circle in a complex plane. The real part of complex-valued degrees represents the amplitude term, while the imaginary part represents the phase term. This property empowers CNRs to model multidimensional variables. Moreover, some interesting properties and useful results have also been proved. Furthermore, the practicality of the proposed concepts is verified by an application, which discusses the use of the proposed concepts in statistical decision-making. Additionally, a comparative analysis between the novel concepts of CNRs and the existing methods is carried out.

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

“…Thus, they can model uncertain events with time periods and phase alterations. Yaqoob et al [35] and Nasir et al [36,37] studied the complex relations and applied them in cellular networks and economic relationships. Ngan et al [38] represented CIFS by quaternion numbers and applied them in decision-making, while Kumar and Bajaj [39] worked on the distance measures and entropies in CIF soft sets.…”

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

“…Garg and Rani [26] put forward the interval-valued complex intuitionistic fuzzy relation (IVCIFS). Li [27] used IFSs for multiattribute decision-making (MD) models and methods; De et al [28] applied IFSs in medical diagnosis; Vlachos and Sergiadis [29] applied IFSs to pattern recognition; Lee et al [30] compared IVFSs, IFSs and bipolar-valued FSs; Grzegorzewski [31] used Hausdorff metric for finding the distances between IVFSs and IFSs; Nasir et al [32][33][34][35] applied complex relations to analysis of economic relationships. Ali et al [36] studied complex intuitionistic fuzzy classes; Liu and Jiang [37] proposed a new distance measure of IVIFSs and applied it in decision making; Bustince and Burillo [38] devised the correlation of IVIFSs; Nayagam and Sivaraman [39] proposed a method of ranking IVIFSs.…”