P-sets is a set pair, it is composed of internal P-set and outer P-set, it has dynamic characteristic. By using structure of P-sets, dependence theorem and identification theorem are proposed in this paper.
By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets （singular rough ...By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets （singular rough sets）. S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class （law equivalence class） that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets （function singular rough sets）. Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification.展开更多
基金Supported by the Natural Science Foundation of Zhumadian, Henan, China(11704)Supported by the National Natural Science Foundation of Shandong Province(60973042)Supported by the Natural Science Foundation of Shandong Province(Y2008F61, Y2008G20)
文摘P-sets is a set pair, it is composed of internal P-set and outer P-set, it has dynamic characteristic. By using structure of P-sets, dependence theorem and identification theorem are proposed in this paper.
基金the National Natural Science Foundation of China (Grant No. 60364001)the key Project of Chinese Ministry of Education (Grant No. 206089)the Natural Science Foundation of Shandong Province of China (Grant No. Y2007H02)
文摘By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets （singular rough sets）. S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class （law equivalence class） that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets （function singular rough sets）. Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification.
