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.