Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized an...Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.展开更多
The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the defin...The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.展开更多
基金supported by the China Postdoctoral Science Foundation(200902321)a Marie Curie International Incoming Fellowship within the 7th European Community Framework Program(FP7-PIIFGA-2013-629051)
文摘Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.
基金The National Natural Science Foundation of China(No.60474022)
文摘The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.
