Kybernetika 28 no. 7, 25-27, 1992

Fuzzy concepts defined via residuated maps

Achille Achache and Arturo A. L. Sangalli


We show how some concepts such as "fuzzy subse'' or "fuzzy closed set of a topological spac'' 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 "ideal'', "subgroup'' and other collections of subsets having a complete lattice structure.


04A72, 03E72, 06A15, 54A40