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Further study of multigranulation T-fuzzy rough sets
Wentao Li1, Xiaoyan Zhang1, Wenxin Sun1
1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China.
This study introduces the pessimistic multigranulation T-fuzzy rough set model, complementing the existing optimistic version. These models offer a more complete framework for T-fuzzy rough set theory and its applications.
Area of Science:
- Fuzzy Set Theory
- Rough Set Theory
- Granular Computing
Background:
- The optimistic multigranulation T-fuzzy rough set model was established in T-fuzzy approximation spaces.
- Further investigation into T-fuzzy approximation spaces is needed.
Purpose of the Study:
- To deeply improve the optimistic multigranulation T-fuzzy rough set model by exploring its properties.
- To establish a complete multigranulation T-fuzzy rough set model by introducing the pessimistic multigranulation T-fuzzy rough set.
- To study the relationships between multigranulation and classical T-fuzzy rough sets.
Main Methods:
- Investigating further properties of the optimistic multigranulation T-fuzzy rough set model.
- Developing the pessimistic multigranulation T-fuzzy rough set model.
- Analyzing the properties of multigranulation T-fuzzy lower and upper approximation operators.
- Examining relationships between multigranulation and classical T-fuzzy rough sets.
Main Results:
- The optimistic multigranulation T-fuzzy rough set model is improved.
- A complete multigranulation T-fuzzy rough set model is constituted by introducing the pessimistic version.
- Key properties of multigranulation T-fuzzy approximation operators are presented.
- The classical T-fuzzy rough set model is shown to be a special case of the new models.
Conclusions:
- The study establishes a comprehensive multigranulation T-fuzzy rough set framework.
- The developed models provide a deeper understanding of T-fuzzy rough set theory.
- A case study illustrates the practical applicability of the optimistic and pessimistic models.
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