Research on Properties of Fuzzy Granular Space
Xuesong Fang · Mohu xitong yu shuxue · 2009
On the basis of Reference [16],we introduced fuzzy granular space into general fuzzy equivalence relations,studied its properties,and get three main conclusions. Firstly,the ordered equivalence relations set is introduced,and four propositions are equivalent as the follows:(1) A fuzzy equivalence relation is given; (2) An equicrural normalized pseudo-metric is given; (3) An ordered granular space is given; (4) An ordered equivalence relations set is given. Secondly,by introducing the projective metric and extending metric of an equicrural normalized pseudo-metric deriving from a fuzzy equivalence relation,the metric on fuzzy granular space is determined,which it is an equicrural normalized metric,and its dynamic properties are discussed. Finally,the relationship between order of fuzzy granular space and one of fuzzy equivalence relation is discussed,which their order are same. There conclusions prefect the fuzzy granular space theory,and further provide a direct and geometric interpretation for granular computing,and will help us for deeper understanding the essence of granular procedure.