A completeness analysis of frequent weighted concept lattices and their algebraic properties

  • Authors:

  • Sulan Zhang;Ping Guo;Jifu Zhang;Xinxin Wang;Witold Pedrycz

  • Affiliations:

  • School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China and School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyu ...;School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China;School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China;School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6R 2V4 and Systems Research Institute, Polish Academy of Sciences, 01-447Warsaw, Poland and School o ...

  • Venue:
  • Data & Knowledge Engineering
  • Year:
  • 2012

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Abstract

Frequent weighted concept lattice (FWCL) is an interesting version of the WCL (weighted concept lattice), which helps realize knowledge extraction in a more efficient way. One of the open issues is that the completeness of FWCL cannot be ensured (namely, some nodes would be removed since their intent weights are lower than intent importance thresholds specified by the user, so that it can occur that the supremum of their parent nodes or the infimum of their child nodes might not exist). In this study, we first introduce a virtual node into the structure of FWCL to retain the completeness of FWCL. Next, an algebraic system of FWCL is presented by introducing two operations, which form the least frequent upper bound and the greatest frequent lower bound of the FWCL. Finally, we discuss some algebraic properties of FWCL and prove its completeness of knowledge representation in this way providing the theoretical foundations for applications of WCL.