Lattice-valued F-transforms and similarity relations

The relationships between lattice-valued F-transforms and similarity relations are investigated. Several similarity relations are naturally associated with F-transforms. Three types of such similarity relations related to lattice-valued F-transforms are investigated: namely, similarity relationships that are related to spaces with fuzzy partitions as ground structures of the F-transform, relationships between extensional hulls with respect to similarity relations and F-transforms, and relationships between similarities of pairs of functions on the one hand and similarities of the F-transforms of these functions on the other. Some examples of possible applications are also presented.