Attribute reductions of quantitative dominance-based neighborhood rough sets with A-stochastic transitivity of fuzzy preference relations

Attribute reductions based on approximate operations have never been proposed in quantitative dominance-based neighborhood rough sets. In this paper, we mainly discuss these problems and present an accelerated process by constructing a particular transitivity of fuzzy preference relations with aggregation operators called A-stochastic transitivity. Firstly, definitions of approximating qualities are given by considering the ordered consistence between condition and decision attributes. Secondly, theories of attribute reductions based on approximate operations are analyzed. Thirdly, the accelerated process of attribute reductions is investigated with A-stochastic transitivity and the algorithm is designed. Moreover, the efficiency of the proposed method is stressed by execution time of attribute reductions, which is evaluated by statistical hypothesis testing on some public data sets. Finally, the effectiveness of our algorithm is verified by comparing results with classical methods in rough set theory and machine learning.