On a continuous lattice approach to modeling of coarse data in system analysis (original) (raw)

We emphasize the need to model rigorously uncertain coarse data in systems such as decision-support systems and intelligent machines. We exemplify the framework of continuous lattices by formulating human perception-based information as coarsening schemes using fuzzy partitions. Specifically, the formal concept of random fuzzy sets is treated as random elements with values in the space of upper semicontinuous functions which is endowed with a continuous lattice structure. As a result, random fuzzy (closed) sets on locally compact, Hausdorfff and second countable spaces are special random elements taking values in separable metric spaces.