Real formal concept analysis based on grey-rough set theory

Authors:
Qiang Wu;Zongtian Liu
Affiliations:
Department of Computer Technology and Science, Shaoxing College of Art and Science, Shaoxing, Zhejiang 312000, PR China and School of Computer Engineering and Science, Shanghai University, Shangha ...;School of Computer Engineering and Science, Shanghai University, Shanghai 200072, PR China
Venue:
Knowledge-Based Systems
Year:
2009

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Abstract

One of the main concepts in grey system theory is how systems should be controlled under incomplete or lack of information situation. Grey number denoting an uncertain value is described in real interval from this concept. In this paper, we introduce the real formal concept analysis based on grey-rough set theory by using grey numbers, instead of binary values. We propose, to extend the notion of Galois connection in a real binary relation as well as the notions of formal concept and Galois lattice. The relationships between the new notions and old ones are discussed. Finally, we present a grey-rough set approach to Galois lattices reduction.