Journal
INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS
Volume 8, Issue 1, Pages 81-94Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s13042-016-0586-z
Keywords
Inconsistent formal decision context; Attribute reduction; Congruence relation; Rough set; Three-way concept analysis
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Funding
- Natural Science Foundation of China [11202187, 61573321, 61202206, 61272021]
- Open Foundation from Marine Science in the Most Important Subjects of Zhejiang
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In this paper, notions and methods of attribute reduction are investigated for an inconsistent formal decision context. Based on congruence relations defined on the object power set, we first introduce notions of distribution attribute reduct and maximum distribution attribute reduct for an inconsistent formal decision context, and discuss their relations in detail. We then define discernibility matrices and discernibility functions associated with the proposed attribute reducts, from which we can calculate all attribute reducts. Finally, we compare the proposed consistent sets with four types of consistent sets in previously published papers. The results show that a distribution consistent set belongs to any of those four types of consistent sets. Therefore, it has all the properties of those four types of consistent sets.
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