http://www.jiyeliang.net/Cms_Data/Contents/SXU_JYL/Folders/JournalPapers/~contents/HCN28MSVKZKVXNQ5/Multigranulation%20decision-theoretic%20rough%20sets(2014)IJAR.pdf

Multigranulation decision-theoretic rough sets

http://www.weihuaxu.com/papers/2015/Concept%20learning%20via%20granular%20computing%20A%20cognitive%20viewpoint.pdf

Concept learning via granular computing

NMGRS: Neighborhood-based multigranulation rough sets

http://www.yuhuaqian.net/Cms_Data/Contents/SXU_YHQ/Folders/JournalPapers/~contents/SW62399HY6J9K898/Multigranulation%20rough%20sets%20from%20partition%20to%20covering.pdf

Multigranulation rough sets: From partition to covering

https://cyberleninka.org/article/n/688210.pdf

A survey on rough set theory and its applications

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and upper approximations of a fuzzy set are defined on multiple fuzzy tolerance relations. It follows the research on the properties of the fuzzy lower and upper approximations of the new models. The fuzzy rough set model, rough set model on a tolerance relation and multi-granulation rough sets models are special cases of the new ones from the perspective of the considered concepts, related relations and granular computing. The new models are meaningful generalizations of the classical rough sets.

http://www.weihuaxu.com/papers/2011/Multi-granulation%20Fuzzy%20Rough%20Sets%20in%20a%20Fuzzy%20Tolerance%20Approximation%20Space.pdf

Multi-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space

The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.

Multi-granulation rough sets based on tolerance relations

Based on analysis of Pawlak's rough set model in the view of single equivalence relation and the theory of fuzzy set, associated with multi-granulation rough set models proposed by Qian, two types of new rough set models are constructed, which are multi-granulation fuzzy rough sets. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzzy rough set models. Then it can be found that the Pawlak rough set model, fuzzy rough set model and multi-granulation rough set models are special cases of the new one from the perspective of the considered concepts and granular computing. The notion of rough measure and α, β-rough measure which are used to measure uncertainty in multi-granulation fuzzy rough sets are introduced and some basic properties of the measures are examined. The construction of the multi-granulation fuzzy rough set model is a meaningful contribution in the view of the generalization of the classical rough set model.

Multi-granulation fuzzy rough sets

A generalized multi-granulation rough set is proposed in this paper. In the new model, supporting characteristic function is defined and a parameter called information level is introduced to investigate that an object supports a concept precisely under majority granulations. Moreover, some important properties are discussed on the new multi-granulation rough set. And it can be found that the proposed model is more valid than old multiple granulation rough set models and Pawlak rough set model.

/pdf/a-generalized-multi-granulation-rough-set-approach-uijwr73hom.pdf

A generalized multi-granulation rough set approach

Based on the analysis of rough set model on a tolerance relation and considering of the theory of fuzzy rough set, two types of new generalized fuzzy rough set models are constructed, which are multi-granulation fuzzy rough sets on tolerance relations. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzzy rough set models on tolerance relations. The fuzzy rough set model and rough set model on a tolerance relation are special cases of the new one from the perspective of the considered concepts and granular computing. The relationships among the fuzzy rough set model, the first MGFRS and the second MGFRS all on tolerance relations are investigated.

/pdf/multi-granulation-fuzzy-rough-set-model-on-tolerance-32yxqomgrb.pdf

Qiaorong Wang

Papers

Multi-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space

Multi-granulation rough sets based on tolerance relations

Multi-granulation fuzzy rough sets

A generalized multi-granulation rough set approach

Multi-granulation fuzzy rough set model on tolerance relations