To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a ...To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.展开更多
In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for...In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.展开更多
The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specifi...The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specified by the principle of discernibility matrix; (2) ID3 can be partly, but not naturally, specified by the principle of discernibility matrix; and (3) The principle of discernibility matrix is employed to analyze Cendrowska sample set, and it shows the weaknesses of knowledge representation style of decision tree in theory.展开更多
Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obta...Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.展开更多
基金supported by the National Natural Science Foundation of China (61403184, 61105082)the ‘1311 Talent Plan’ of Nanjing University of Posts and Telecommunications (NY2013)+3 种基金the ‘Qinglan’ Project of Jiangsu Province (QL2016)the Natural Science Foundation of Nanjing University of Posts and Telecommunications (215149)the Priority Academic Program Development of Jiangsu Higher Education Institutions, (PAPD)the Major Program of the Natural Science Foundation of Jiangsu Province Education Commission (17KJA120001)
文摘To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.
文摘In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.
基金This research is partly supported by the National '863' High-Tech Programme (No. 863-306-ZT06-07-1)and NKPSF (G1998030508).
文摘The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specified by the principle of discernibility matrix; (2) ID3 can be partly, but not naturally, specified by the principle of discernibility matrix; and (3) The principle of discernibility matrix is employed to analyze Cendrowska sample set, and it shows the weaknesses of knowledge representation style of decision tree in theory.
基金supported by the Foundation and Frontier Technologies Research Plan Projects of Henan Province of China under Grant No. 102300410266
文摘Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.
