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AIMS Mathematics

2026, Volume 11, Issue 6: 16174-16198. doi: 10.3934/math.2026665
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Research article

A multi-granulation T-rough set model and its properties

  • School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
  • Published: 08 June 2026

  • MSC : 03B52, 03E72, 06D72, 54A40, 94D05

  • This paper works in the setting of multi-granulation rough sets on two universes. We combine multi-granulation ideas with set-valued mappings and introduce a multi-granulation T-rough set model built on set-valued mappings. Four inverse approximation operators are defined: a pessimistic upper inverse operator, a pessimistic lower inverse operator, an optimistic upper inverse operator, and an optimistic lower inverse operator. Using these operators, we set up a two-universe framework for multi-granulation T-rough sets. We then spell out the basic properties of the operators, prove several theorems, and clarify how the different operators relate to each other. A few examples are included to show how the model works in practice. The model extends rough set theory on two universes and gives a new way to describe information that comes from multiple sources and multiple granular levels.

    Citation: Weihua Lin. A multi-granulation T-rough set model and its properties[J]. AIMS Mathematics, 2026, 11(6): 16174-16198. doi: 10.3934/math.2026665

    Related Papers:

  • This paper works in the setting of multi-granulation rough sets on two universes. We combine multi-granulation ideas with set-valued mappings and introduce a multi-granulation T-rough set model built on set-valued mappings. Four inverse approximation operators are defined: a pessimistic upper inverse operator, a pessimistic lower inverse operator, an optimistic upper inverse operator, and an optimistic lower inverse operator. Using these operators, we set up a two-universe framework for multi-granulation T-rough sets. We then spell out the basic properties of the operators, prove several theorems, and clarify how the different operators relate to each other. A few examples are included to show how the model works in practice. The model extends rough set theory on two universes and gives a new way to describe information that comes from multiple sources and multiple granular levels.



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  • © 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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