Soft Computing

, Volume 15, Issue 6, pp 1115-1128

First online:

Rule acquisition and attribute reduction in real decision formal contexts

  • Hong-Zhi YangAffiliated withFaculty of Science, Xi’an Jiaotong University
  • , Leung YeeAffiliated withDepartment of Geography and Resource Management, Center for Environmental Policy and Resource Management, University of Hong KongInstitute of Space and Earth Information Science, The Chinese University of Hong Kong
  • , Ming-Wen ShaoAffiliated withCollege of Information Science and Technology, Shihezi University Email author 

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Formal Concept Analysis of real set formal contexts is a generalization of classical formal contexts. By dividing the attributes into condition attributes and decision attributes, the notion of real decision formal contexts is introduced. Based on an implication mapping, problems of rule acquisition and attribute reduction of real decision formal contexts are examined. The extraction of “if–then” rules from the real decision formal contexts, and the approach to attribute reduction of the real decision formal contexts are discussed. By the proposed approach, attributes which are non-essential to the maximal s rules or l rules (to be defined later in the text) can be removed. Furthermore, discernibility matrices and discernibility functions for computing the attribute reducts of the real decision formal contexts are constructed to determine all attribute reducts of the real set formal contexts without affecting the results of the acquired maximal s rules or l rules.


Attribute reduction Concept lattice Formal concept analysis Real relation Rules acquisition