Real formal concept analysis based on grey-rough set theory

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.