Interval forecasts evaluation can be reduced to examining the unconditional coverage and independence properties of the hit sequence. A new class of exact independence tests for the hit sequence and a definition for tendency to clustering of violations are proposed. The tests are suitable for detecting models with a tendency to generate clusters of violations and are based on an exact distribut...

The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characteristic polynomial. A condition is derived using certain known facts about matrix minors and its chara...

Techniques enabling decision makers to identify a set of non-mutually exclusive projects (or alternatives) constituting a portfolio, while allowing for imprecise information with respect to projects’ benefits, costs, and overall resource constraints, have emerged as an area of great applicability. To reach applicability, reasonable and computationally meaningful decision evaluation methods are ...

| The more complex the problem, the more complex the system necessary for solving this problem. For very complex problems, it is no longer possible to design the corresponding system on a single resolution level, it becomes necessary to have multiresolutional systems. When analyzing such systems { e.g., when estimating their performance and/or their intelligence { it is reasonable to use the mu...

This paper deals with characterizing the connected component AS(~a) of a set S that contains a given point ~a. The set S is assumed to be de…ned by nonlinear inequalities, so that interval analysis can be used to prove that a given box is inside or outside S. Further, the characterization of AS(~a) is used to …nd a feasible path (i.e. a path that lies within S) that links ~a to any other point ...

We consider a class of arithmetic equations over the complete lattice of integers (extended with−∞ and∞) and provide a polynomial time algorithm for computing least solutions. For systems of equations with addition and least upper bounds, this algorithm is a smooth generalization of the Bellman-Ford algorithm for computing the single source shortest path in presence of positive and negative edg...

In this paper we present a mathematical model for archetypal analysis of data represented by means of intervals of real numbers. We extend the model for single-valued data proposed in the pioneering work of Cutler and Breiman on this topic. The core problem is a non-convex optimization one, which we solve by means of a sequential quadratic programming method. We show numerical experiments perfo...

A standard for the notation of the most used quantities and operators in interval analysis is proposed.