Fuzzy concepts defined via residuated maps

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library 1 We show how some concepts such as "fuzzy subset" or "fuzzy closed set of a topological space" may be identified with certain maps between complete lattices. Underlying this representation is the fact that the category of closure spaces contains the category of complete lattices and residuated maps as a reflective subcategory. This approach suggests a uniform method for fuzzifying concepts such as "ideals", "subgroups" and other collections of subsets having a complete lattice structure.