An approach to [Formula: see text]-single-valued neutrosophic submodules

Area of Science:

• Mathematics
• Algebraic Structures
• Fuzzy Set Theory

Background:

• Erroneous and complex information requires advanced handling methods.
• Single-valued neutrosophic sets (svns) offer a framework for quantifying indeterminacy.
• svns extend fuzzy and intuitionistic fuzzy set theories with independent membership components.

Purpose of the Study:

• To investigate [Formula: see text]-single-valued neutrosophic sets ([Formula: see text]-svns).
• To establish the relationship between [Formula: see text]-svns and [Formula: see text]-single-valued neutrosophic modules/submodules.
• To analyze the algebraic structures of [Formula: see text]-single-valued neutrosophic submodules within classical modules.

Main Methods:

• Development of the [Formula: see text]-svns concept.
• Relating [Formula: see text]-svns to algebraic module theory.
• Analysis of algebraic structures using neutrosophic set principles.

Main Results:

• Introduction of [Formula: see text]-svns and their connection to neutrosophic modules.
• Comprehension of the algebraic structures of [Formula: see text]-single-valued neutrosophic submodules.
• Demonstration of enhanced generalizability compared to prior methods.

Conclusions:

• The proposed [Formula: see text]-svns framework provides a generalized approach to handling complex data in algebraic structures.
• This research enhances the understanding and application of neutrosophic set theory in module theory.
• The developed strategies offer a more versatile toolset for mathematical analysis involving uncertainty.