Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order....Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order. Being called the reduct problem, this algorithm can be regarded as a mapping R = Reduct(S) from the attribute order space Theta to the reduct space R for an information system <U, C boolean OR D>, where U is the universe and C and D are two sets of condition and decision attributes respectively. This paper focuses on the reverse problem of reduct problem S = Order(R), i.e., for a given reduct R of an information system, we determine the solution of S = Order(R) in the space Theta. First, we need to prove that there is at least one attribute order S such that S = Order(R). Then, some decision rules are proposed, which can be used directly to decide whether the pair of attribute orders has the same reduct. The main method is based on the fact that an attribute order can be transformed into another one by moving the attribute for limited times. Thus, the decision of the pair of attribute orders can be altered to the decision of the sequence of neighboring pairs of attribute orders. Therefore, the basic theorem of neighboring pair of attribute orders is first proved, then, the decision theorem of attribute order is proved accordingly by the second attribute.展开更多
One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of...One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.展开更多
By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute dis...By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.展开更多
There are similarities and differences about the order of the attributes between English sentences and Chinese sentenc es. As a result, mistakes can often be observed; those mistakes are the results of unfamiliarity w...There are similarities and differences about the order of the attributes between English sentences and Chinese sentenc es. As a result, mistakes can often be observed; those mistakes are the results of unfamiliarity with the proper order of the attri butes. But here, special attention is paid to the EST(English for Science and Technology) translation in which their differences are much more distinct. Generally speaking, the attributes in English can be divided into pre-attributes and post-attributes in terms of their positions in a sentence. But in Chinese an attribute is usually put before a noun, and rarely put after it, so several simple comparisons are tried to find out some rules to translate English attributes into Chinese.展开更多
文摘Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order. Being called the reduct problem, this algorithm can be regarded as a mapping R = Reduct(S) from the attribute order space Theta to the reduct space R for an information system <U, C boolean OR D>, where U is the universe and C and D are two sets of condition and decision attributes respectively. This paper focuses on the reverse problem of reduct problem S = Order(R), i.e., for a given reduct R of an information system, we determine the solution of S = Order(R) in the space Theta. First, we need to prove that there is at least one attribute order S such that S = Order(R). Then, some decision rules are proposed, which can be used directly to decide whether the pair of attribute orders has the same reduct. The main method is based on the fact that an attribute order can be transformed into another one by moving the attribute for limited times. Thus, the decision of the pair of attribute orders can be altered to the decision of the sequence of neighboring pairs of attribute orders. Therefore, the basic theorem of neighboring pair of attribute orders is first proved, then, the decision theorem of attribute order is proved accordingly by the second attribute.
基金Supported by the National Natural Science Foundation of China under Grant No. 60175023 and the National Basic Research 973 Program of China under Grant No. 2004CB318103
文摘One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.
基金Foundation item： Supported by the Nature Science Foundation of Shandong Province（Y2007H02）
文摘By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.
文摘There are similarities and differences about the order of the attributes between English sentences and Chinese sentenc es. As a result, mistakes can often be observed; those mistakes are the results of unfamiliarity with the proper order of the attri butes. But here, special attention is paid to the EST(English for Science and Technology) translation in which their differences are much more distinct. Generally speaking, the attributes in English can be divided into pre-attributes and post-attributes in terms of their positions in a sentence. But in Chinese an attribute is usually put before a noun, and rarely put after it, so several simple comparisons are tried to find out some rules to translate English attributes into Chinese.
