We prove that, determines a sequence of positive fuzzy numbers.
The operations sequencing sub-problem determines a sequence of operations on all the machines.
If no fixed point is found along the way, the process determines a sequence of telescopic squares which uniquely identifies a point.
(18) Therefore, (13), (18) and since (L_{n,alpha}), (R_{n,alpha}) are left continuous, we have that ([L_{n,alpha},R_{n,alpha}]) determines a sequence of positive fuzzy numbers (x_{n}) such that (11) holds.
As in statement (i), using (3.10), (3.11), (3.15)–(3.24), (3.24), Theorem 2.1 and working inductively, we get that the positive solution,,, of (3.17), determines a sequence of positive fuzzy numbers, such that (3.27) holds.
Therefore, since,, are left continuous and (3.22), (3.23), (3.25), (3.26) are satisfied, from Theorem 2.1, we get that the positive solution,,, of (3.17), with initial values,,, satisfying (3.11), (3.12), (3.14), determines a sequence of positive fuzzy numbers, such that (3.27).
