Complex fermatean neutrosophic graph and application to decision making

Said Broumi; Swaminathan  Mohanaselvi; Tomasz  Witczak; Mohamed  Talea; Assia  Bakali; Florentin  Smarandache

doi:10.31181/dmame24022023b

Authors

Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco https://orcid.org/0000-0002-1334-5759
Swaminathan Mohanaselvi Department of Mathematics, SRM Institute of Science and Technology Kattankulathur-603203, India https://orcid.org/0000-0003-4197-3856
Tomasz Witczak Institute of Mathematics, Faculty of Science and Technology, University of Silesia, Bankowa 14, 40-007 Katowice, Poland https://orcid.org/0000-0002-1178-3691
Mohamed Talea Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco https://orcid.org/0000-0003-2364-0804
Assia Bakali Ecole Royale Navale-Boulevard Sour Jdid, Morocco https://orcid.org/0000-0002-2764-9745
Florentin Smarandache Department of Mathematics,University of New Mexico,705 Gurley Avenue, Gallup, NM 87301, USA https://orcid.org/0000-0002-5560-5926

DOI:

https://doi.org/10.31181/dmame24022023b

Keywords:

Complex neutrosophic sets, Complex fermatean Neutrosophic sets, Neutrosophic graphs, Complex Fermatean neutrosophic graph.

Abstract

A new growing area of neutrosophic set (NS) 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 take 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. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesian product of CFNG. Moreover, the concept of regular graph under complex fermatean neutrosophic environment is discussed. Finally, an application of multi criteria decision making problem in educational system to evaluate lecturer’s research productivity using CFNG is discussed.

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