Our "augmentation" terminology does not mean to suggest that the intervals themselves are larger, just that the top and bottom elements of the corresponding closed intervals are longer.

As always in posets, the closed interval [[sigma], [tau]] in P is the set {[pi] | [sigma] [less than or equal to] [pi] [less than or equal to] [tau]}, and the open interval ([sigma], [tau]) (the interior of [[sigma], [tau]]) is the set {[pi] | [sigma] < [pi] < [tau]}, where "<" and "[less than or equal to]" have the usual meaning.

defines a binary operation on the set of closed intervals.

Hence the closed interval A represents an uncertain number x [member of] [[a.

We denote the set of all real valued

closed intervals by IR.

Because the stress S and strength R are functions of these interval variables respectively, they will vary within some closed intervals [S.

Assume that x denotes an uncertain parameter in the structural reliability problem, and it varies within a closed interval [x.

n] that can be defined as the Cartesian product of n

closed intervals.

can not explain ranking between two overlapping closed intervals.

Using the AI index we have presented the ordering for closed intervals reflecting decision maker's preference as

This article is dedicated to the investigation of the topological properties of the order complex of the proper part of closed intervals in a Cambrian semilattice.

gamma]]) to closed intervals of the weak order yields a lattice homomorphism (and hence a lattice congruence).