The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at ho...The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at home and abroad have studied it and obtained a lot of results. Now the theory of Rough sets is still progressing rapidly. However, when this theory is applied to describing an information system, the indiscernibility展开更多
Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyz...Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.展开更多
文摘The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at home and abroad have studied it and obtained a lot of results. Now the theory of Rough sets is still progressing rapidly. However, when this theory is applied to describing an information system, the indiscernibility
基金the Scientific Research and Development Project of Shandong Provincial Education Department(J06P01)the Science and Technology Fundation of University of Jinan (XKY0703).
文摘Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
