Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough se...Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough sets.First,we present belief and plausibility functions in covering information systems and study their properties.With these measures we characterize lower and upper approximation operators and attribute reductions in covering information systems and decision systems respectively.With these discussions we propose a basic framework of numerical characterizations of covering rough sets.展开更多
In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief ...In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.展开更多
In rough set theory,the lower and upper approximation operators are important notions defined by a binary relation.In this paper,we introduce a general type of relation-based fuzzy rough model determined by a triangul...In rough set theory,the lower and upper approximation operators are important notions defined by a binary relation.In this paper,we introduce a general type of relation-based fuzzy rough model determined by a triangular norm.Properties of fuzzy rough approximation operators are examined.The fuzzy rough approximation operators are also characterized by axioms.A comparative study of the fuzzy rough set algebra with other mathematical structures such as fuzzy topological spaces,fuzzy measurable spaces,and fuzzy belief structures is investigated.展开更多
基金supported by a grant of NSFC(70871036)a grant of National Basic Research Program of China(2009CB219801-3)
文摘Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough sets.First,we present belief and plausibility functions in covering information systems and study their properties.With these measures we characterize lower and upper approximation operators and attribute reductions in covering information systems and decision systems respectively.With these discussions we propose a basic framework of numerical characterizations of covering rough sets.
基金NationalNaturalScienceFoundationofChina (No .60373078)
文摘In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.
基金supported by grants from the National Natural Science Foundation of China(Nos.60673096 and 60773174)the Natural Science Foundation of Zhejiang Province in China(No.Y107262).
文摘In rough set theory,the lower and upper approximation operators are important notions defined by a binary relation.In this paper,we introduce a general type of relation-based fuzzy rough model determined by a triangular norm.Properties of fuzzy rough approximation operators are examined.The fuzzy rough approximation operators are also characterized by axioms.A comparative study of the fuzzy rough set algebra with other mathematical structures such as fuzzy topological spaces,fuzzy measurable spaces,and fuzzy belief structures is investigated.
