Neutrosophic Sets and Systems
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, 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.
Recommended Citation
Rajesh, K.; S. Moorthy; A. Jeeva; and D. Moganraj. "Application of the Neutrosophic Fuzzy Sets in Profession Determination." Neutrosophic Sets and Systems 81, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol81/iss1/37
