Set-theoretic relations for metasets

Abstract

ABSTRACTThe paper introduces partial set-theoretic relations for metasets and investigates their properties. Metaset is a concept of imprecise set designed to represent vague notions in Artificial Intelligence, whose idea stems from Boolean-valued techniques in classical set theory. The basic set relations are extended to functions valued in a Boolean algebra or unit interval. Important classical set theory axioms: extensionality and comprehension are formulated for metasets. The latter enables formal definitions of collections with blurred boundaries by using set-theory formulae. This facilitates representing and reasoning about imprecise data.