Abstract
Attribute reduction is a challenging problem in rough set theory, which has been applied in many research fields, including knowledge representation, machine learning, and artificial intelligence. The main objective of attribute reduction is to obtain a minimal attribute subset that can retain the same classification or discernibility properties as the original information system. Recently, many attribute reduction algorithms, such as positive region preservation, generalized decision preservation, and distribution preservation, have been proposed. The existing attribute reduction algorithms for generalized decision preservation are mainly based on the discernibility matrix and are, thus, computationally very expensive and hard to use in large-scale and high-dimensional data sets. To overcome this problem, we introduce the similarity degree for generalized decision preservation. On this basis, the inner and outer significance measures are proposed. By using heuristic strategies, we develop two quick reduction algorithms for generalized decision preservation. Finally, theoretical and experimental results show that the proposed heuristic reduction algorithms are effective and efficient.
Highlights
Originating from the mathematician Pawlak in the early 1980s, rough set theory (RST) [1]has been regarded as an effective tool for the processing of inconsistent or uncertain information.It has been extensively utilized in research fields such as uncertainty reasoning [2,3], knowledge representation [4], feature selection, and machine learning [5,6,7]
We carried out the comparative experiments from three aspects: The first aspect was to verify monotonicity of the similarity degree; the second aspect was to validate the correctness of the proposed algorithms; and the third aspect was to illustrate the efficiency of the proposed algorithms
Developing efficient algorithms for attribute reduction for decision systems is an important issue in many research fields, such as knowledge representation, multiple attribute decision making, and artificial intelligence
Summary
Originating from the mathematician Pawlak in the early 1980s, rough set theory (RST) [1]. Compared with the heuristic attribute reduction methods MIBR [14] and QUICKREDUCT [24], the algorithm RSFSACO, based on ant colony optimization, proposed by Chen et al [29] could obtain a minimal reduct in most cases. Objects with the same condition attribute values may have different decision values To keep these decision values unchanged, Miao et al [12] proposed an attribute reduction method for generalized decision preservation based on the discernibility matrix. The time complexity of the discernibility matrix-based reduction algorithm for generalized decision preservation (DMRAG) proposed by dm/2e.
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