Rough逻辑及其在数据约简中的应用

Rough Logic and Its Applications in Data Reduction

讨论了被定义在邻域值决策表上的 Rough逻辑及其公式的真值 ,它在数据约简中的应用比 Pawlak定义的决策表上的决策逻辑更加广泛 .目前常用的数据约简方法有 Pawlak的数据分析和 Skowron的分明矩阵法 .前者是非形式的 ,不易机械化 ;而后者虽说直观、易理解 ,但还要求生成一个分明矩阵的中间环节 ,从而造成时空上的不必要的开销 .采取一边从邻域值决策表关于属性值邻域是分明的属性并构成邻域分明合取范式 ,一边做这种逻辑公式的等价变换直接得到邻域值决策表的诸多约简 .由于不用生成分明矩阵的中间环节 ,这样便节省了空间和时间 ,提高了运行效率 .对此 ,对拥有 6个属性 (4个条件和两个决策属性 )以及 10 2个个体的一致决策表或邻域值决策表进行处理并生成了约简的决策规则 .用两种不同方法在 P 2 33/ 6 4 M的微机上用 DELPHI3.0分别对它们进行约简并得到相同的结果 ,采用一边从表中提取公式一边做约简的方法 ,所用时间约 1分 54秒 ;而用分明矩阵法却耗去 1分 55秒 .由于增加了一个数组 (分明矩阵 ) ,便增加了空间复杂度 O(m× n2 ) ,其中 m为属性数 ,n为个体数 ,随着属性数和个体数的增加 ,所占的空间和时间也将急剧增加 .可见 ,从空间和时间消耗上来看 ,这两种方法的优劣是十分明显的 .

The rough logic defined on neighbor valued decision tables and its truth values of the formulas are discussed in this paper. It is more general than the decision logic defined by Pawlak in the applications of data reduction. At present, the methods used are often Pawlak's data analysis and Skowron's discernible matrix methods. The former is informal, no ease mechanization. The latter is intuitive, easy to understand, but it requires to generate a medial link of discernible matrix, to make unnecessary expenses on time and space. Therefore, in the paper, one side extracts the attributes of attribute neighbor valued discernible from the neighbor valued decision table and discernible Conjunctive Normal Form is constructed. The other side simplifies the formula to use absorbable laws and other calculus of logical formulas. It obtains directly all reductions in the neighbor valued decision table. Since it doesn't need to generate the medial link of discernible matrix, so it can spare space and time, and raise the efficiency of the program run. Thus, reduction of the tables is handled to possess 6 attributes (4 conditional attributes and 2 decision attributes) and 102 objects to use two methods respectively, and to obtain the same results. It uses one side to extract formulas from the tables, and the other side to reduce the formulas in DELPHI 3.0 on P ⅠⅠ 233/64 M. The time of program running is about 1 minute 54 seconds; while time of spending is about 1 minute 55 seconds to use the discernible matrix method. Due to the increase of an array (discernible matrix), its space degree of complexity is O(m×n 2) , where m is the number of attributes, n is the number of objects. So, the space and time occupied will also increase rapidly along with the increment of attributes and objects. The strong points and shortcomings of two methods are quite clear from space and time used.