In this paper,a novel definition of entropy is introduced. It is used for measuring the uncertainty of roughness of knowledge in tolerant rough sets. In addition ,we prove that the entropy of knowledge decreases monot...In this paper,a novel definition of entropy is introduced. It is used for measuring the uncertainty of roughness of knowledge in tolerant rough sets. In addition ,we prove that the entropy of knowledge decreases monotonously as the granularity of information becomes smaller. Then,a new reduction algorithm based on entropy is developed.Simulation results show that the algorithm can find the minimal reduction in most cases.展开更多
Reduction of attributes is one of important topics in the research on rough set theory. Wong S K M and Ziarko W have proved that finding the minimal attribute reduction of decision table is a NP-hard problem. Algorith...Reduction of attributes is one of important topics in the research on rough set theory. Wong S K M and Ziarko W have proved that finding the minimal attribute reduction of decision table is a NP-hard problem. Algorithm A (the improved algorithm to Jelonek) choices optimal candidate attribute by using approximation quality of single attribute,it improves efficiency of attribute reduction,but yet exists the main drawback that the single atribute having maximum approxiamtion quality is probably optimal candidate attribute. Therefore,in this paper, we introduce the concept of compatible decision rule,and propose an attribute reduction algorithm based on rules (ARABR). Algorithm ARABR provides a new method that measures the relevance between extending attribute and the set of present attributes, the method assures that the optimal attribute is extended, and obviously reduces the search space. Theory analysis shows that algorithm ARABR is of lower computational complexity than Jelonek's algorithm,and overcomes effectively the main drawback of algorithm A.展开更多
文摘In this paper,a novel definition of entropy is introduced. It is used for measuring the uncertainty of roughness of knowledge in tolerant rough sets. In addition ,we prove that the entropy of knowledge decreases monotonously as the granularity of information becomes smaller. Then,a new reduction algorithm based on entropy is developed.Simulation results show that the algorithm can find the minimal reduction in most cases.
文摘Reduction of attributes is one of important topics in the research on rough set theory. Wong S K M and Ziarko W have proved that finding the minimal attribute reduction of decision table is a NP-hard problem. Algorithm A (the improved algorithm to Jelonek) choices optimal candidate attribute by using approximation quality of single attribute,it improves efficiency of attribute reduction,but yet exists the main drawback that the single atribute having maximum approxiamtion quality is probably optimal candidate attribute. Therefore,in this paper, we introduce the concept of compatible decision rule,and propose an attribute reduction algorithm based on rules (ARABR). Algorithm ARABR provides a new method that measures the relevance between extending attribute and the set of present attributes, the method assures that the optimal attribute is extended, and obviously reduces the search space. Theory analysis shows that algorithm ARABR is of lower computational complexity than Jelonek's algorithm,and overcomes effectively the main drawback of algorithm A.
