A Study On Some Problems Of Reduction Based On Rough Set

Rough set theory, which simulates the capability of granulation and approximation in human cognition, is an effective mathematical tool to deal with those uncertainly; inconsistency, ambiguity data. In recently years, attribute reduction based on Rough Set becomes a very hot research direction. There are many researches interested in Rough Set, because attribute reduction based on Rough Set plays an important role in machine learning, data mining and pattern recognition. In fact, there are a lot of factors such as uncertainly, inconsistency, ambiguity and so on. Therefore they lead to be more difficult for attribute reduction in real-world and not to be widely used and applied in the related fields because of the complexity of attribute reduction. In this paper, we firstly introduce some algorithms that have been known at home and abroad about attribute reduction based on Rough Set. And secondly, we have some new explorations about attribute reduction algorithm based on neighborhood rough set model and distribution reduction algorithm in inconsistent information system and distribution reduction based inconsistent neighborhood rough set model.First, we design an attribute reduction algorithm based on neighborhood rough set model with higher and quicker efficiency. Because there is a big difference between classic rough set and neighborhood rough set model in attribute reduction, the latter leads to many algorithms for classic rough set that are not suitable for neighborhood rough set model. And because a lot of time is spent in computing distance between two samples in neighborhood rough set model, it leads to the lower efficiency comparing with attribute reduction based on classic rough set. It is a big bottleneck that how to reduce the number of comparison among samples and narrow the searching space to quickly find the neighbor of sample for designing a quick reduction algorithm based neighborhood rough set model. In order to reduce the searching space when we find the neighbor, in this paper, we split the whole data set that we want to reduce into different slices at first, and cluster those records that are more nearer each other into the same slice, and the neighbor of records that are in a slice always contains records of itself and two adjacent slices, this is proved by us in the follow paper. So, in order to find the neighbor of records in a slice, we can only search records of itself and the two adjacent slices, because the searching space is only the three slices instead of the whole data set, it leads to the time efficiency of algorithm significantly improved. Second, we propose a distribution reduction algorithm in inconsistent information system. Compare to discemibility matrix, it is a more effective algorithm. In general, Rough Set is based on indiscernibility relation and is defined as the operations of set, according to introducing the notion of upper approximation and lower approximation. This always is called the algebraic point of Rough Set Theory. However, some researchers have study Rough Set Theory by Information Theory, and give the idea of Information Theory for Rough Set Theory. So, it is another choice to attribute reduction in Information Theory of Rough Set Theory. In this paper, according to the relationship between Rough Set Theory and Information Theory, the conditional entropy based criteria is adopted to select proper attribute distribution reduction in inconsistent information system, the quick distribution reduction algorithm proposed in this paper employees a hash based heuristic backward greedy policy.At last, it is possible to face the problem of distributed attribute reduction based inconsistent information system and attribute reduction based neighborhood rough set model, when we reduce the information system. It is necessary to solve it for us. In this section, we will mainly discuss about distributed attribute reduction in discemibility matrix algorithm and backward greedy algorithm based on conditional entropy in inconsistent neighborhood rough set model.