Though many hierarchical structures have been proposed to analyze the finer or coarser relationships between two granulation spaces, these structures can only be used to compare the single granulation spaces. However,...Though many hierarchical structures have been proposed to analyze the finer or coarser relationships between two granulation spaces, these structures can only be used to compare the single granulation spaces. However, it should be noticed that the concept of multigranulation plays a fundamental role in the development of granular computing. Therefore, the comparison between two multigranulation spaces has become a necessity. To solve such problem, two types of the multigranulation spaces are considered： one is the partition-based multigranulation space, the other is the covering-based multigranulation space. Three different hierarchical structures are then proposed on such two multigranulation spaces, respectively. Not only the properties about these hierarchical structures are discussed, but also the relationships between these hierarchical structures and the multigranulation rough sets are deeply investigated. It is shown that the first hierarchical structure is consistent with the monotonic varieties of optimistic multigranulation rough set, and the second hierarchical structure is consistent to the monotonic varieties of pessimistic multigranulation rough set, the third hierarchical structure is consistent to the monotonic varieties of both optimistic and pessimistic multigranulation rough sets.展开更多
Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consis...Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consistent blocks are used to construct multigranulation rough sets. Not only are the basic properties about these models studied, but also the relationships between different multigranulation rough sets are explored. It is shown that by using maximal consistent blocks, the greater lower approximation and the same upper approximation as from tolerance relations can be obtained. Such a result is consistent with that of a single-granulation framework.展开更多
With granular computing point of view,this paper first presents a novel rough set model with a multigranulation view,called pessimistic rough decision,where set approximations are defined through using consistent gran...With granular computing point of view,this paper first presents a novel rough set model with a multigranulation view,called pessimistic rough decision,where set approximations are defined through using consistent granules among multiple granular spaces on the universe.Then,we investigate several important properties of the pessimistic rough decision model.With introduction of the rough set model,we have developed two types of multigranulation rough sets(MGRS):optimistic rough decision and pessimistic rough decision. These multigranulation rough set models provide a kind of effective approach for problem solving in the context of multi granulations.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61100116,61103133the Natural Science Foundation of Jiangsu Province of China under Grant No.BK2011492+2 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No.11KJB520004the Postdoctoral Science Foundation of China under Grant No. 20100481149the Postdoctoral Science Foundation of Jiangsu Province of China under Grant No.1101137C
文摘Though many hierarchical structures have been proposed to analyze the finer or coarser relationships between two granulation spaces, these structures can only be used to compare the single granulation spaces. However, it should be noticed that the concept of multigranulation plays a fundamental role in the development of granular computing. Therefore, the comparison between two multigranulation spaces has become a necessity. To solve such problem, two types of the multigranulation spaces are considered： one is the partition-based multigranulation space, the other is the covering-based multigranulation space. Three different hierarchical structures are then proposed on such two multigranulation spaces, respectively. Not only the properties about these hierarchical structures are discussed, but also the relationships between these hierarchical structures and the multigranulation rough sets are deeply investigated. It is shown that the first hierarchical structure is consistent with the monotonic varieties of optimistic multigranulation rough set, and the second hierarchical structure is consistent to the monotonic varieties of pessimistic multigranulation rough set, the third hierarchical structure is consistent to the monotonic varieties of both optimistic and pessimistic multigranulation rough sets.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 61170165, 61100116, 61272419, 61373062）, Natural Science Foundation of Jiangsu Province of China （BK2011492, BK2012700, BK20130471）, Qing Lan Project of JiangsuProvince of China, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information （Nanjing University of Science and Tech- nology）, Ministry of Education （30920130122005）, Key Laboratory of Arti- ficial Intelligence of Sichuan Province （2013RYJ03）, Natural Science Foun- dation of Jiangsu Higher Education Institutions of China （13KJB520003, 13KJD520008）.
文摘Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consistent blocks are used to construct multigranulation rough sets. Not only are the basic properties about these models studied, but also the relationships between different multigranulation rough sets are explored. It is shown that by using maximal consistent blocks, the greater lower approximation and the same upper approximation as from tolerance relations can be obtained. Such a result is consistent with that of a single-granulation framework.
基金supported by grants from the National Natural Science Foundation of China(Nos.60903110, 60773133 and 70971080)the Natural Science Foundation of Shanxi Province in China(Nos.2009021017-1, 2008011038).
文摘With granular computing point of view,this paper first presents a novel rough set model with a multigranulation view,called pessimistic rough decision,where set approximations are defined through using consistent granules among multiple granular spaces on the universe.Then,we investigate several important properties of the pessimistic rough decision model.With introduction of the rough set model,we have developed two types of multigranulation rough sets(MGRS):optimistic rough decision and pessimistic rough decision. These multigranulation rough set models provide a kind of effective approach for problem solving in the context of multi granulations.
