Study On Multi-granulation Fuzzy Decision-theoretic Rough Sets

This paper combines multi-granulation rough sets with fuzzy decision-theoretic rough sets,studying the sequential three-way decision of tolerance-based multi-granularity fuzzy decision-theoretic rough sets,and discussing the multi-granulation fuzzy decision-theoretic rough sets in multiset-valued information tables.In the fuzzy decision system,firstly,the multi-granulation fuzzy rough sets of tolerance-based is introduced,on this basis,a multi-granulation fuzzy decision-theoretic rough sets of tolerance-based is proposed.Secondly,the sequential three-way decision of tolerance-based fuzzy decision-theoretic rough sets is extended from single-granulation model to multi-granulation model,and some related properties are studied.Then we give the definition of uncertainty measure:precision and coarseness,and discuss some basic prop-erties.Finally,in the optimistic case,a reduction method of sequential three-way decision of tolerance-based multi-granularity fuzzy decision-theoretic rough sets is given and an example is used to verify its effectiveness and feasibility.In the multiset-valued information tables,it combines the multi-granulation rough sets with the fuzzy decision-theoretic rough sets.Firstly,the upper and lower approxi-mations under optimistic,pessimistic and mean conditions are proposed and some relat-ed properties are studied.Secondly,the concepts of accuracy and coarseness of multi-granulation fuzzy decision-theoretic rough sets are given and some basic properties are discussed.Finally,an example is given to verify their effectiveness.