Fuzzy sets as texture spaces, II.: Subtextures and quotient textures

In this paper the authors introduce the notions of subtexture and quotient texture of a complemented texture space. Conditions ensuring the existence of such textures are discussed, and applied to show that certain natural subtextures of product textures may be defined. These are used in particular to give representations of product it-fuzzy sets, and a representation involving quotient textures is also examined. (C) 2000 Elsevier Science B.V. All rights reserved.