A Continuous Lattice Approach to Random Sets

Hung T. Nguyen

Abstract

This paper is about modeling of coarse data in statistics using set-valued random elements. We consider also the case of fuzzy set-valued random elements for modeling of perception-based information. These are typically random elements with values in some functional spaces. Unlike the standard approach in stochastic processes, we emphasize the lattice approach leading to compact, separable metric spaces.