On reduction of attributes in inconsistent decision tables based on information entropies and stripped quotient sets.

• We propose a proposal for attribute reduction based on stripped quotient sets. • The proposed proposal has solid theoretical background and efficient algorithms. • The proposed proposal reports the superior results when compared to the state-of-the-art methods. Data scenarios on nowadays comprise an enormous number of attributes and instances while not all attributes are necessary and useful for data analytics and knowledge extraction in framing expert and intelligent systems. In such scenarios, removing irrelevant and redundant attributes is a very important task and a challenging research problem. In rough set approach, the attribute reduction method based on the positive region has reported the promising performance in consistent decision tables, while conditional information entropies are employed instead for inconsistent decision tables. However, the complexity of existing methods is still quite high. This paper proposes efficient attribute reduction approaches in inconsistent decision tables by using the concept of stripped quotient sets. Firstly, we present a method for fast determining reducts based on the conditional information entropies including Shannon's and Liang's entropies, called ERED-SQS. Secondly, we define an original notion of attribute reduction based on the stripped quotient set and propose an efficient SRED algorithm to cope with this reduct type. Finally, a simulation performed on 16 datasets varying in a number of objects, up to 5 millions, and a number of attributes, up to 20 thousands, to validate the proposed methods in comparison with the state-of-the-art methods. Experimental results show that the proposed algorithms, ERED-SQS and SRED, have significantly improved the computational time, especially for large data sets. Moreover, the classification accuracy of the reducts obtained from SRED algorithm outperforms that of the reducts based on Shannons and Liangs conditional entropies. This verifies that our proposal is applicable and effective to applications regarding attribute reduction in inconsistent decision tables. [ABSTRACT FROM AUTHOR]