This paper is an attempt to address the processing of nonlinear numerical constraints over the Reals by combining three different methods: local consistency techniques, symbolic rewriting and interval methods. To formalize this combination, we define a generic two-step constraint processing technique based on an extension of the Constraint Satisfaction Problem, called Extended Constraint Satisf...

This paper compares various implementations of the parameter partitioning methods (PPS-methods) for optimal outer estimation of the solution sets to interval linear systems. Special attention is focused on the analysis of the modification based on Rohn’s technique, which is the most complex, laborious, but the most efficient one. We present results of numerical experiments with several computat...

This paper presents adaptive and non-adaptive fuzzy c-means clustering methods for partitioning symbolic interval data. The proposed methods furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. Moreover, various cluster interpretation tools are introduced. Experiments with real an...

How to estimate parameters from observations subject to errors and uncertainty? Very often, the measurement errors are random quantities that can be adequately described by the probability theory. When we know that the measurement errors are normally distributed with zero mean, then the (asymptotically optimal) Maximum Likelihood Method leads to the popular least squares estimates. In many situ...

Indexing video content is one of the most important problems in video databases. In this paper we present linear time and space algorithms for handling video metadata that represent objects or events present in various frames of the video sequence. To accomplish this, we make a straightforward reduction of this problem to the intersection problem in Computational Geometry. Our first result is a...

Conclusions This paper describes a novel technique, based on interval methods, for the estimation of reliability using fault trees. The approach encodes inherent uncertainty in the input data by modeling this data in terms of intervals. Appropriate interval arithmetic is then used to propagate the data through standard fault trees to generate output distributions which reflect the uncertainty i...

Some recent research has confirmed that the standard Wald (normal) confidence interval approximation for the binomial proportion is inadequate in key respects, especially for extreme values of p . Even for moderately large values of n the coverage probabilities can prove to be erratic for various specific values of p . This fact makes general rules for the use of the Wald method problematic. Al...

The interval-Newton approach provides the power to solve nonlinear equation solving and global optimization problems with complete mathematical and computational certainty. The primary drawback to this approach is that computation time requirements may become quite high. In this paper, a strategy for using linear programming (LP) techniques to improve computational efficiency is considered. In ...

A simulation study was conducted to provide a more thorough account of measurement error associated with interval sampling methods. A computer program simulated the application of momentary time sampling, partial-interval recording, and whole-interval recording methods on target events randomly distributed across an observation period. The simulation yielded measures of error for multiple combi...

We study the performance of affine arithmetic as a replacement for interval arithmetic in interval methods for ray casting implicit surfaces. Affine arithmetic is a variant of interval arithmetic designed to handle the dependency problem, and which has improved several interval algorithms in computer graphics.