We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,i...We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.展开更多
Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy se...Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approxima- tion operators of vague sets based on vague relations, and investigate the basic properties of approximation opera- tors on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transi- tive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.展开更多
Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuri...Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.展开更多
文摘We review and compare two definitions of rough set approximations.One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe.The latter definition,although less studied,is semantically superior for interpreting rule induction and is closely related to granularity switching in granular computing.Numerical measures about the accuracy and quality of approximations are examined.Several semantics difficulties are commented.
文摘Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approxima- tion operators of vague sets based on vague relations, and investigate the basic properties of approximation opera- tors on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transi- tive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.
基金supported by the National Natural Science Foundation of China (61472056, 61309014)
文摘Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.
