JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (5): 32-45.doi: 10.6040/j.issn.1671-9352.c.2020.004

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Concept reduction of preserving binary relations based on Boolean matrix

XIE Xiao-xian1, LI Jin-jin1,2*, CHEN Dong-xiao1, LIN Rong-de1,3   

  1. 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian, China;
    2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China;
    3. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian, China
  • Published:2020-05-06

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Abstract: The problems of concept characteristics and concept reduction preserving binary relations are studied by Boolean matrix operation. Firstly, formal context is described as a Boolean matrix, the relation matrices of object\attribute are generated by using the binary relation matrix, and their related properties are studied. Further, concept characteristics of three different types of concepts in the processing of concept reduction are obtained by using Boolean matrix operation. Finally, the minimum operation of concept interval sets is done with Boolean matrix operation, the discernibility matrix is simplified, and a method of calculating concept reduction is given. Compared with the existed methods of concept reduction in formal context, the proposed matrix algorithm is simple and its time complexity is lower.

Key words: formal context, formal concept, Boolean matrix, reduction, characteristic

CLC Number: 

  • TP18
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