Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices

The purpose of this paper is to interpret fuzzy Kripke models as fuzzy information systems with objects and attributes. We introduce topological structures (interior, closure operators, Alexandrov pretopologies, Alexandrov precotopologies, fuzzy rough set) to the formulas of fuzzy Kripke models based on complete residuated lattices. We study the relations of possible worlds as objects and formulas as attributes in a fuzzy information system. Using the properties of residuated and Galois connections, we can obtain fuzzy concept lattices and formal fuzzy concept lattices. We give their examples.