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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 836137, 9 pages
http://dx.doi.org/10.1155/2014/836137
Research Article

Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

1School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
2Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China

Received 9 April 2014; Revised 9 June 2014; Accepted 11 June 2014; Published 30 June 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 Li Yang and Yang Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.