| In this paper,novel multi-granulation hesitant fuzzy decision-theoretic rough sets models are developed by researching fuzzy sets and rough sets to explore multi-granulation hesitant fuzzy decision-theoretic rough sets under hesitant fuzzy order information system.In the hesitant fuzzy approximation space,multi-granulation hesitant fuzzy decision-theoretic rough sets are proposed by combining multi-granulation rough sets and decision-theoretic rough sets,analysing their properties and investigating the relationship between multi-granulation rough sets from the viewpoint of multi-granulation.A three-way de-cisions are introduced in multi-granulation hesitant fuzzy decision-theoretic rough sets and the decision rules are derived by Bayes decision.Moreover,two types rough mem-bership degree and uncertainty measures are presented,analyzing their properties,and the approach of attribute reduction are established for the multi-granulation consistency hesitant fuzzy decision-theoretic rough sets.Covering-based multi-granulation hesitant fuzzy decision-theoretic rough sets are dis-cussed by integrating hesitant fuzzy sets and decision-theoretic rough sets.Moreover,the definition of lower and upper approximation are depicted as well as the basic properties are considered.Further,the correlation between the presented models are discussed and the corresponding three-way decisions are given. |
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