@article{Lin2026, 
author = {Weihua Lin},
title = {A multi-granulation T-rough set model and its properties},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16174-16198},
keywords = {T-rough sets, multi-granulation, set-valued mapping, inverse operator, pessimistic operator, optimistic operator},
url = {https://www.sciopen.com/article/10.3934/math.2026665},
doi = {10.3934/math.2026665},
abstract = {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.}
}