Analysis of the Major Investment Object by Using a Novel Approach Based on Neutrosophic Information

Area of Science:

• Mathematics
• Graph Theory
• Fuzzy Set Theory

Background:

• Neutrosophic sets (NS) provide a framework for uncertainty using association, neutral, and nonassociation degrees.
• Neutrosophic graphs (NGs) and single-valued NGs (SVNGs) handle complex information, with degrees being crucial for applications.
• Existing methods face challenges in decision-making, pattern recognition, and network analysis due to information complexity.

Purpose of the Study:

• To develop novel forms of edge irregular single-valued neutrosophic graphs (EISVNGs).
• To introduce highly edge irregular SVNGs (HEISVNGs) and strongly edge irregular SVNGs (SEISVNGs).
• To apply these novel graph structures to decision-making problems.

Main Methods:

• Development of definitions, theorems, and mathematical proofs for various edge irregular SVNGs.
• Modeling two types of decision-making problems using the proposed neutrosophic graph framework.
• Utilizing computational processes to validate the proposed graph structures and their applications.

Main Results:

• Successfully defined and characterized various forms of edge irregular SVNGs, including HEISVNGs and SEISVNGs.
• Demonstrated the applicability of these novel graph structures in solving decision-making problems.
• Computational validation confirmed the efficacy of the proposed edge irregular neutrosophic graphical structures.

Conclusions:

• Edge irregular neutrosophic graphical structures provide an effective tool for addressing decision-making problems with uncertainty.
• The proposed framework offers advantages over existing methodologies, as shown through comparative analysis.
• This research advances the application of neutrosophic graph theory in practical problem-solving.