Consider a sorting problem in which we do not know the numbers exactly. Instead, for each number, we know an interval on the real line to which it belongs.
That is, we are givennclosed intervals of the formŒa
i;bi
,whereai bi.We
wish tofuzzy-sortthese intervals, i.e., to produce a permutation hi1;i2;:::;iniof
the intervals such that for j D1;2;:::;n, there exist cj 2Œa
ij
;bij
 satisfying
c1c2 cn.

Question

Consider a sorting problem in which we do not know the numbers exactly. Instead, for each number, we know an interval on the real line to which it belongs.
That is, we are givennclosed intervals of the formŒa
i;bi
,whereai bi.We
wish tofuzzy-sortthese intervals, i.e., to produce a permutation hi1;i2;:::;iniof
the intervals such that for j D1;2;:::;n, there exist cj 2Œa
ij
;bij
 satisfying
c1c2 cn.