Fuzzy sets as texture spaces, I.: Representation theorems

The authors continue the development of a theory of texture spaces, introducing complemented products and sums, and applying these in a series of representation theorems for fuzzy lattices and the lattices of L-fuzzy sets, generalized fuzzy sets and intuitionistic sets. The second paper in this series will extend this enquiry by introducing subtextures and quotient textures and a second series of papers is under preparation which consider topological aspects of this correspondence. (C) 2000 Elsevier Science B.V. All rights reserved.