On the neutrosophic soft set with rough set theory
Minakhi Das1, Debadutta Mohanty2, Kedar Chandra Parida3
1Department of Mathematics, North Orissa University, Mayurbhanj, Odisha India.
This study introduces neutrosophic soft rough sets, a novel framework combining rough set theory, soft set theory, and neutrosophic set theory. It enhances the ability to manage uncertain and imprecise information in complex systems.
Area of Science:
- Mathematics
- Computer Science
- Information Theory
Background:
- Rough set theory effectively addresses uncertainty, incompleteness, and imprecision.
- Soft set theory and neutrosophic set theory offer advanced methods for handling uncertain, incomplete, and inconsistent information.
- Existing theories have limitations in fully integrating these concepts.
Purpose of the Study:
- To expand the theoretical scope of rough set, soft set, and neutrosophic set theories.
- To introduce a new concept of neutrosophic soft set with roughness, without relying on the full soft set.
- To establish foundational definitions, properties, and examples for the proposed neutrosophic soft rough set.
Main Methods:
- Integration of rough set theory with neutrosophic set theory and soft set concepts.
- Development of a modified neutrosophic soft set framework incorporating roughness.
- Formal definition of neutrosophic soft rough set and exploration of its basic characteristics.
Main Results:
- Introduction of the neutrosophic soft rough set concept.
- Establishment of key definitions and properties for the new set structure.
- Demonstration of the framework's applicability through examples and analysis of dispensability and equalities.
Conclusions:
- The neutrosophic soft rough set provides a robust mathematical framework for handling complex uncertain data.
- This novel approach extends the capabilities of existing theories in information processing.
- The established properties and examples pave the way for future research and applications.
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