Approaches to attribute reduction in concept lattices induced by axialities

  • Authors:

  • Ju-Sheng Mi;Yee Leung;Wei-Zhi Wu

  • Affiliations:

  • College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, PR China;Department of Geography and Resource Management, Center for Environmental Policy and Resource Management and Institute of Space and Earth Information Science, The Chinese University of Hong Kong, ...;School of Mathematics, Physics, and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, PR China

  • Venue:
  • Knowledge-Based Systems
  • Year:
  • 2010

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Abstract

This paper investigates approaches to attribute reduction in concept lattices induced by axialities. Based on an axiality, a type of covariant Galois connection between power sets, or equivalently a binary relation between the ground sets, the lattice of all concepts associated with a formal context is studied. Some judgment theorems for attribute reduction in such a lattice are proposed and proved. Extended from the idea of knowledge reduction in rough set theory, a Boolean approach to calculating all reducts of a context is formulated via the use of discernibility function. Finally, all attributes are classified into three types by their significance in constructing the concept lattice. The characteristics of these types of attributes are also analyzed.