Real world data analysis is often affected by different type of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data (parameters). The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering, rather than a single value for each data, the interval of values in which it may fall: the in...

In this paper, the average cases of Markov decision processes with uncertainty is considered. That is, a controlled Markov set-chain model with a finite state and action space is developed by an interval arithmetic analysis, and we will find a Pareto optimal policy which maximizes the average expected rewards over all stationary policies under a new partial order. The Pareto optimal policies is...

In this paper, we present and discuss a new interval-based method of reliability estimation using fault trees for the case of uncertain and time-varying input reliability data. The approach is based on the generation of output distributions (probability estimates with appropriate ranges of uncertainty) which preserve the effects of uncertainty in the input (component or subsystem-level) data. T...

arcs in the set Z Of (1.1). These applications divide naturally into two classes. In the rst class, H models a parametrized physical system, which we wish to study as the parameter varies, such as in [12]. In the second class, we introduce an articial parameter in order to solve (or nd all solutions to) a system of n nonlinear equations in n unknowns for which locally convergent methods are ...

Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. Recent work explored some operators for deciding how multiple such judgments should be aggregated. Here, we generalize this line of study by introducing a family of operators called interval aggregation methods, which contain existing operato...

For SLAM problem [3], building an accurate map leads to an accurate localization. We propose a guaranteed solution using interval methods for nonlinear observation model to work with holnomic robots with no rotation, where the map is proven to converge. Our approach does not require any assumptions with regard to the linearity of the observation model, nor its noise except that it needs to be b...

Interval analysis is a powerful tool which allows to design branch-and-bound algorithms able to solve many global optimization problems. In this paper we present new adaptive multisection rules which enable the algorithm to choose the proper multisection type depending on simple heuristic decision rules. Moreover, for the selection of the next box to be subdivided, we investigate new criteria. ...

This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights...