COMPLEX FERMATEAN NEUTROSOPHIC GRAPH AND APPLICATION TO DECISION MAKING

Abstract

A new growing area of the neutrosophic set theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS takes values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established and various basic graphical ideas such as the order, size, degree and total degree of a vertex of it are introduced. Also, set theoretical operations such as complement, union, join, ring-sum and cartesian product of CFNG are studied. Further, the concept of a regular graph under a complex fermatean neutrosophic environment is introduced. Finally, we make use of the proposed CFNG in solving a multi-criteria decision-making problem in which the graphical structure of attributes is uncertain. This study also demonstrates the application of a CFNG in the educational system to evaluate a lecturer's research productivity.