Abstract
Attribute reduction is an important topic in the research of rough set theory, and it has been widely used in many aspects. Reduction based on an identifiable matrix is a common method, but a lot of space is occupied by repetitive and redundant identifiable attribute sets. Therefore, a new method for attribute reduction is proposed, which compresses and stores the identifiable attribute set by a discernibility information tree. In this paper, the discernibility information tree based on a lower approximation identifiable matrix is constructed in an inconsistent decision information system under dominance relations. Then, combining the lower approximation function with the discernibility information tree, a complete algorithm of lower approximation reduction based on the discernibility information tree is established. Finally, the rationality and correctness of this method are verified by an example.
Highlights
Rough set theory [1], as a new mathematical tool, is mainly used to deal with imprecise, inconsistent, and incomplete information
In the discernibility information tree based on the lower approximation identifiable matrix, the union of identifiable attribute sets which are corresponding to paths with only one node constitutes the core
We will construct the discernibility information tree under the dominance relation according to the steps of Algorithm 1 and implement the lower approximation reduction based on this tree in the inconsistent ordered decision information system
Summary
Rough set theory [1], as a new mathematical tool, is mainly used to deal with imprecise, inconsistent, and incomplete information. Jankowski et al [11] analyzed the impact of online advertising on advertising effect and user experience and proposed a balanced method of advertising resource development based on fuzzy multi-objective modeling In these aspects, and in other areas, rough set theory plays an important role, such as in pattern recognition, machine learning, intelligent control and other fields [12,13,14,15,16,17]. For the attribute sets with the same prefix, take { a, b, c, d} and { a, b} for example, when the two paths occur simultaneously, the path of the attribute set with fewer elements { a, b} is selected to replace the path of { a, b, c, d}, and the path of { a, b} is mapped onto the discernibility information tree, which reduces the space occupation of redundant elements Based on this tree, the algorithm of approximation reduction is established.
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