# Linear Interval Tolerance Problem and Linear Programming Techniques

Linear Interval Tolerance Problem and Linear Programming Techniques In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ∑∀∃([A], [b]) = {x ∈ R n | ∀A ∈ [A], ∃b ∈ [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ∑∀∃([A], [b]), and we provide a new definition of the optimality of an interval vector included in ∑∀∃([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ∑∀∃([A], [b]). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Linear Interval Tolerance Problem and Linear Programming Techniques

, Volume 7 (6) – Oct 3, 2004
15 pages

/lp/springer_journal/linear-interval-tolerance-problem-and-linear-programming-techniques-24JGcSwk0i
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1014758201565
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ∑∀∃([A], [b]) = {x ∈ R n | ∀A ∈ [A], ∃b ∈ [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ∑∀∃([A], [b]), and we provide a new definition of the optimality of an interval vector included in ∑∀∃([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ∑∀∃([A], [b]).

### Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

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