Affiliations: [a] School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, P. R. China | [b] School of Electrical Engineering, Northwest MinZu University, Lanzhou, Gansu, P. R. China
Correspondence:
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Corresponding author. Haidong Zhang, School of Mathematics and Computer Science, Northwest MinZu University,
Lanzhou, Gansu, P. R. China. Tel./Fax: +86 9314512202; E-mails: [email protected].
Abstract: Through a combination of hesitant fuzzy sets with rough sets, this study develops a single-granulation hesitant fuzzy rough set model from the perspective of granular computing. In the multi-granulation framework, we propose two types of multi-granulation rough set model, called the optimistic multi-granulation hesitant fuzzy rough sets and pessimistic multi-granulation hesitant fuzzy rough sets. In the models, the multi-granulation hesitant fuzzy lower and upper approximations are defined based on multiple hesitant fuzzy tolerance relations. The relationships among the single-granulation hesitant fuzzy rough sets, optimistic multi-granulation hesitant fuzzy rough sets and pessimistic multi-granulation hesitant fuzzy rough sets are also investigated. Finally, we develop an approximation reduction approach of multi-granulation hesitant fuzzy rough sets to eliminate redundant hesitant fuzzy granulations with a detailed example.
