Interval-representation of sets: Dempster-Pawlak-Turksen schema

Dempster, Pawlak, and Turksen schema can be re-structured to generate interval-valued Type 2 fuzzy sets, with suitable modifications to Dempster´s multi-valued maps and Pawlak´s rough sets. In this restructuring, we investigate Turksen´s interpretation of Zadeh´s CWW that generate interval-valued Type 2 fuzzy sets. First, it can be shown that there is a natural transformation between Dempster´s and Pawlak´s construction schemas. Secondly, Dempster´s and Pawlak´s upper set formulation schema is modified. Thirdly, multi-valued maps are restricted to a special well known subset of information granules. This modification and restriction forms the "Dempster-Pawlak-Zadeh" unification (Turksen, 2001). With this unification, we generate FDCF and FCCF expressions for concept combinations in Zadeh´s CWW with the application of linguistic operators such as "AND", "OR", etc. Finally, it is proposed that the combinations of concepts formulated in this manner be a formulation for the CWW.