| 摘要: |
| Pawlak教授提出的粗糙集理论是解决集合边界不确定的重要手段,他构建了边界不确定集合的两条精确边界,但没有给出用已有知识基来精确或近似地构建目标概念(集合)X的方法.在前期的研究中提出了寻找目标概念X的近似集方法,但并没有给出最优的近似集.首先,回顾了集合间的相似度概念和粗糙集的近似集Rλ(X)的构建方法,提出并证明了Rλ(X)所满足的运算性质.其次,找到了Rλ(X)比上近似集R(X)和下近似集R(X)更近似于目标概念X的λ成立的区间.最后,提出了R0.5(X)作为目标概念的最优近似集所满足的条件. |
| 关键词: 粗糙集 模糊集 近似集 相似度 粒计算 |
| DOI：10.13328/j.cnki.jos.004854 |
| 分类号: |
| 基金项目:国家自然科学基金(61472056, 61272060); 重庆市自然科学基金(cstc2012jjA40032, cstc2013jcyjA40063) |
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| Optimal Approximation Sets of Rough Sets |
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ZHANG Qing-Hua1,2, XUE Yu-Bin1, WANG Guo-Yin2
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1.School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;2.Chongqing Key Laboratory of Computational Intelligence Chongqing University of Posts and Telecommunications, Chongqing 400065, China
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| Abstract: |
| Rough set theory proposed by professor Pawlak is an important mean to solve the problem of uncertain boundary region. Pawlak constructed two crisp boundaries for the set with uncertainty boundary but did not give any exact or approximate methods of using the existing knowledge base to build an approximation set of a target concept .In order to solve this problem, in the previous researches a method for looking for this kind of approximation target concept (set) is proposed. However, that method does not give out a kind of optimal approximation set. In this paper, firstly, the concept of the similarity between the target set and its approximation set and the method for constructing approximation set of rough set are reviewed, and the operation properties are proposed and proved respectively. Secondly, an interval of λ is found, and in this interval Rλ(X) is more similar to the target concept X than the upper-approximation set R(X) or lower-approximation set R(X). Finally, the conditions of R0.5(X) as an optimal approximation set of the target concept X are proposed. |
| Key words: rough set fuzzy set approximation set similarity granular computing |
