This paper deals with the problem of computing the shortest reducts of a decision system. The shortest reducts are useful for attribute reduction in classification problems and data size reduction. Unfortunately, finding all the shortest reducts is an NP-hard problem. There are some algorithms reported in the literature to overcome the complexity of computing the shortest reducts. However, most of these algorithms relay on costly operations for candidate evaluation. In this paper, we propose a new algorithm for computing all the shortest reducts; based on binary cumulative operations over a pair-wise comparison matrix, and a fast candidate evaluation process. Binary cumulative operations save computation time by avoiding repetitive calculations. Furthermore, unlike other algorithms reported in the literature, our candidate evaluation process relays on low-cost operations which reduce the runtime in most cases. Our experiments over synthetic and real-world decision systems show that our proposal is faster than state of the art algorithms in most decision systems.

本文涉及计算决策系统最短约简的问题。最短的缩减对于减少分类问题中的属性和减少数据大小很有用。不幸的是，找到所有最短的减价是一个NP难题。文献中报道了一些算法来克服计算最短归约的复杂性。但是，大多数这些算法都依靠昂贵的操作来进行候选者评估。在本文中，我们提出了一种用于计算所有最短归约的新算法。基于成对比较矩阵上的二进制累加运算，以及快速的候选者评估过程。二进制累加运算避免了重复计算，从而节省了计算时间。此外，与文献中报道的其他算法不同，我们的候选评估流程会转而采用低成本操作，从而在大多数情况下减少了运行时间。我们对综合决策系统和现实决策系统的实验表明，我们的建议比大多数决策系统中的最新算法要快。