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Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making
Anjan Mukherjee1, Abhik Mukherjee2
1Department of Mathematics, Tripura University, Suryamaninagar, Agartala, 799022 India.
Annals of Data Science
|April 16, 2024
Summary
This study introduces interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets), a novel mathematical tool for handling uncertain data in fields like economics and medical science. It explores their properties and applications in decision-making problems.
Area of Science:
- Decision Sciences
- Computer Science
- Mathematics
Background:
- Classical mathematical methods struggle with real-world uncertain data.
- Fuzzy sets, rough sets, and soft sets are existing theories for uncertainty, each with limitations.
- Intuitionistic fuzzy rough sets (IFrough sets) were previously proposed to model uncertainty.
Purpose of the Study:
- To introduce the novel concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets).
- To investigate the properties of IVIFS rough approximation operators.
- To explore basic operations and properties of IVIFS rough sets.
Main Methods:
- Development of the interval-valued intuitionistic fuzzy soft rough set framework.
- Analysis of the properties of associated approximation operators.
- Examination of fundamental set operations and their characteristics.
Main Results:
- The paper defines IVIFS rough sets and their approximation operators.
- Key properties of these operators are investigated and established.
- Basic operations and their behaviors within the IVIFS rough set model are studied.
Conclusions:
- The proposed IVIFS rough sets offer a new mathematical tool for uncertainty.
- The study provides a theoretical foundation for IVIFS rough sets and their applications.
- Demonstrated utility in decision-making problems highlights the practical relevance of this new framework.
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