Abstract
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.
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Supported by the National Natural Science Foundation of China (Grant No. 60364001), the key Project of Chinese Ministry of Education (Grant No. 206089), and the Natural Science Foundation of Shandong Province of China (Grant No. Y2007H02)
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Shi, K., Yao, B. Function S-rough sets and law identification. Sci. China Ser. F-Inf. Sci. 51, 499–510 (2008). https://doi.org/10.1007/s11432-008-0050-0
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DOI: https://doi.org/10.1007/s11432-008-0050-0