Topological Information Systems in a Complete Co-Residuated Lattice

In this paper, we introduce topological information systems between objects with a distance and attributes with a distance based on a complete co-residuated lattice. We can obtain two distances and Alexandrov topologies for objects and attributes from an information system. Moreover, we investigate the relations between residuated frames and residuated connections on Alexandrov topologies induced by distances instead of fuzzy equalities. We define a fuzzy concept lattice based on Alexandrov topologies and show that it is a complete lattice. We study its properties as a topological viewpoint and provide examples. Moreover, we introduce R-R embedding maps and R-R frame embedding maps.