JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (8): 60-67.doi: 10.6040/j.issn.1671-9352.0.2022.055

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Complementary concepts and their properties and generation in FCA

HAN Pei-lei1,2, WEI Ling1,2*, WANG Zhen1,2, ZHAO Si-yu1,2,3   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
    3. School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • Online:2022-08-20 Published:2022-06-29

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Abstract: In formal concept analysis, partial order relation of concept lattice describes generalization and specialization between concepts. There also exists some specific semantic information that is worth studying between incomparable concepts. Inspired by this, complementary concepts are studied in this paper. Firstly, the complementary degree of two object subsets is described by considering a specific attribute subset in formal context, based on which the strong and weak complementary relations are defined according to different actual needs. Further, the complementary concepts and their related properties are studied, and the optimal strong complementary concept and optimal weak complementary concept are explored under different semantics, and the corresponding algorithms are also given. Finally, examples are presented given to illustrate the rationality and applicability of the content of this paper.

Key words: concept lattice, formal concept analysis, strong complementary concept, weak complementary concept

CLC Number: 

  • TP18
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