Spherical Fermatean Neutrosophic Topology

P. Roopadevi; M. Karpagadevi; S. Gomathi; S. Krishnaprakash; Said Broumi

Authors

P. Roopadevi Department of Mathematics, Sri GVG Visalakshi College for Women, India
M. Karpagadevi Department of Mathematics, Sri GVG Visalakshi College for Women, India
S. Gomathi Department of Mathematics, Sri GVG Visalakshi College for Women, India
S. Krishnaprakash Department of Mathematics, Sri Krishna College of Engineering and Technology, India
Said Broumi Laboratory of Information Processing, Faculty of Science Ben MSik, University Hassan II, Casablanca

Keywords:

Neutrosophic topology, SFNTS, DoN, DoM, Between zero

Abstract

In this paper, we introduce Spherical Fermatean Neutrosophic Topological Spaces (SFNTS), ex
panding on neutrosophic sets characterized by Degrees of Membership (DoM), Degrees of Indeterminacy (DoI)
and Degrees of Non-Membership (DoN). Fermatean neutrosophic sets in a universe satisfy the conditions where
the sum of the cubes of the DoM and DoN is between zero and one and the cube of the DoI is between zero
and one. The DoM, DoI and DoN are represented accordingly. We de ne a Spherical Fermatean Neutrosophic
Set (SFNS) as a set where each element consists of an element in the universe, along with its DoM, DoN, DoI
and a radius. The DoM, DoN, DoI and the radius are functions mapping the universe to the interval from
zero to one. We extend this to a topological framework by de ning an SFNTS on a set. We also studied
the properties of the SFN closure and SFN interior operators, provided numerical examples and presented a
geometric representation of SFNTS. Additionally, we explored the separation of two SFNSs, the intersection of
two SFNSs and the overlapping of two SFNSs.