Application of the Neutrosophic Fuzzy Sets in Profession  Determination

K. Rajesh; S. Moorthy; A. Jeeva; D. Moganraj

Authors

K. Rajesh Department of Mathematics, Pachaiyappa’s College for Men, Kanchipuram, Tamil Nadu – 631 501, India.
S. Moorthy Department of Mathematics, Government Arts and Science College for Women, Bargur, Krishnagiri, Tamil Nadu – 635 108.
A. Jeeva Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Avadi, Chennai, India – 600 062.
D. Moganraj Department of Mathematics, Government Arts and Science College for Women, Bargur, Krishnagiri, Tamil Nadu – 635 108.

Keywords:

Intuitionistic-FS (IFS), Temporal-IFS (TIFS), Neutrosophic Set (NS), Interval Valued-IFS (IVIFS) and IV-Temporal NFS (IVTNFS).

Abstract

We present several operations, such as algebraic sum, algebraic product, and arithmetic mean,
over the neutrosophic sets extended with moment in time and sketch numbers. Through mathematical
illustrations, we explore various properties and apply this concept to professional decision-making.
Existing neutrosophic set (NS) and fuzzy set theories lack the capability to dynamically account for time
and evolving circumstances. Many approaches fail to provide satisfactory solutions for handling
evolving decision criteria or dynamic uncertainties. While operations like algebraic sum, algebraic
product, and arithmetic mean exist for neutrosophic sets, their adaptation and extension to dynamic and
temporal dimensions (moment in time and sketch numbers) remain underexplored. Additionally, there
is a lack of studies applying neutrosophic set extensions in critical domains such as professional decision
making, which involves dynamic and complex evaluation processes. Many existing models do not
adequately demonstrate practical applicability with robust mathematical illustrations. The introduction
of Interval-Valued Temporal Neutrosophic Fuzzy Sets (IVTNFS), incorporating advanced operations and
additional dimensions, provides a stronger framework for addressing evolving uncertainties in decision
making.

DOI: 10.5281/zenodo.14868296