Abstract: Aiming at the difficulties of the form transferring on large datasets to get reducts, a same element conversion reduction algorithm based on discernibility matrix and discernibility function is put forward. It uses discernibility matrix to keep all classification information of data set, and discernibility function constructs the mathematical logic form from the classical information. The algorithm begins from lower rank of Conjunctive Normal Form(CNF) into Disjunctive Normal Form(DNF). According to the same element conversion algorithm and high element absorption algorithm, if higher ranks are absorbed, the algorithm can return; else the algorithm can enter itself to next circle. Calculation results show that this algorithm greatly reduces the once scale of transform, neatly uses the mature recursive algorithm and works compactly and effectively.

Key words: reduction algorithm, breadth search, discernibility matrix, discernibility function, normal form conversion, rough set

摘要： 针对较大数据集在区分函数范式转换获得约简解集时的困难性，提出一种基于区分矩阵与区分函数的同元转换约简算法。利用区分矩阵保留数据集的全部分类信息，使用区分函数建立分类信息的数学逻辑范式，从低元的合取范式分步转换为析取范式，根据同元转换算法和高元吸收算法，若能够吸收完全则回退，否则再次调用算法进入转换运算。实例演算结果表明，该算法能缩小一次转换规模，灵活地运用递归算法，使得运算简洁有效。

关键词: 约简算法, 广度搜索, 区分矩阵, 区分函数, 范式转换, 粗糙集

CLC Number: 

• TP301.6