The problem of set approximation in incomplete data is addressed.
Different with complete data where the upper/lower approximation of an object
set is certain and can be given by one set, for incomplete data upper/lower
approximation of a set is uncertain and needs to be bracketed by a set pair.
From the completion view of incomplete data, the semantic interpretations of
four boundaries used to approximate a set in incomplete data are given. It is
illustrated that existing definitions based on tolerance class or covering are
not enough to describe precisely the set approximation in incomplete data. Based
on a concept of interval granule, new methods are presented for incomplete data
to compute the four approximation boundaries of a set. This study provides a
new view of granular computing on set approximation in incomplete data and is
helpful for computing the uncertainty of a set more accurately.