Several mathematical frameworks for static analysis of programs have been developed in the past decades. Although these tools are quite useful, they have still many limitations. In particular, integer multivariate polynomials arise in many situations while analyzing programs, and analysis systems are unable to handle such expressions. Although some dedicated methods have already been proposed, ...

Survey data are initially presented as a micro file consisting of the necessary sampling design variables. Then the desired point-estimates as well as the interval estimates can be correctly computed. If several survey data files are available, and the results are needed for comparison, a usual way is to look at those estimates and to interpret the results in the best way possible. If there are...

This paper presents a new numerical algorithm based on interval analysis able to verify that a continuously differentiable function is injective. The efficiency of the method is demonstrated by illustrative examples. These examples have been treated by a C++ solver which is made available.

Including the range of a rational function over an interval is an important problem in numerical computation. A direct interval arithmetic evaluation of a formula for the function yields in general a superset with an error linear in the width of the interval. Special formulas like the centered forms yield a better approximation with a quadratic error. Alefeld posed the question whether in gener...

Proving that an uncertain parametric model is stable amounts to prove the inclusion of two sets: the set A of all feasible parameters and the set B of all parameters for which the model is stable. In this paper, a new algorithm, able to decide whether or not A is included in B, is presented. The method is based on interval analysis which is a numerical tool able to deal with inequalities in a g...

A new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), has recently been proposed. Mohc exploits monotonicity of functions to better filter variable domains. Embedded in an interval-based solver, Mohc shows very high performance for solving systems of numerical constraints (equations or inequalities) over the reals. However, the main drawback is that its revi...

We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominance: interval estimates of quantiles of the error di...

We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B ⊆ Rn is a product of closed real intervals and f : B → Rn is a real-valued continuous function given in the form of arithmetical expressions. The algorithm cleanly separates numerical from combinatorial computation. Based on this, the numerical part provably computes only the information that is strictly ne...

The aim of this paper is to develop some new 2-tuple linguistic hybrid aggregation operators, which are called the extended 2-tuple linguistic hybrid arithmetical weighted (ET-LHAW) operator, the extended 2-tuple linguistic hybrid geometric mean (ET-LHGM) operator, the induced ET-LHAW (IET-LHAW) operator and the induced ET-LHGM (IET-LHGM) operator. These operators do not only consider the impor...

One-sided con&dence intervals in the binomial, negative binomial, and Poisson distributions are considered. It is shown that the standard Wald interval su4ers from a serious systematic bias in the coverage and so does the one-sided score interval. Alternative con&dence intervals with better performance are considered. The coverage and length properties of the con&dence intervals are compared th...