The Belief Structure And Attribute Reduction Of Multi-granulation Fuzzy Rough Approximation Space

Rough set theory is a mathematical tool to effectively deal with incomplete and uncertain data.It is widely used in the fields of artificial intelligence and data mining.In recent years,the combination of fuzzy sets and rough sets to study the uncertainty in practical problems has become one of the main trends of rough set research.The classical rough set theory is based on the equivalence relation(granulation),but a single granulation space can not be used to describe the concept of multiple perspectives in the theory of granular computing.The proposal of multi-granulation can effectively solve this problem,to make multi-granulation model more applicable to practical data,and to improve the applicability of the model,the fuzzy concept is employed in multi-granulation model.In this thesis a multi-granulation fuzzy rough set model is constructed based on classical and fuzzy relation,optimistic and pessimistic upper and lower approximation of multi-granulation fuzzy rough sets are given.Combining with the decomposition theorem of fuzzy sets,the multi-granulation fuzzy rough sets are expressed as a cluster of classical sets.A classical and a fuzzy belief structure are established.The belief function and probability function are constructed based on the upper and lower approximations of the multi-granulation fuzzy rough set under the trust structure,an example shows that the upper and lower approximate probability values of the optimistic multi-granulation fuzzy rough set can not be used as the measure of the belief function and the probability function.A reduction of multi-granulation fuzzy rough set is explored,and a reduction algorithm is formulated.