Exact real arithmetic for interval number systems

Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

From Coinductive Proofs to Exact Real Arithmetic

We give a coinductive characterization of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded...

Analysis of linear mechanical structures with uncertainties by means of interval methods

One of the simplest ways of representation of uncertain or inexact data, as well as inexact computations with them, is based on interval arithmetic. In this approach, an uncertain (real) number is represented by an interval (a continuous bounded subset) of real numbers which presumably contains the unknown exact value of the number in question. Despite its simplicity, it conforms very well to m...

Robust and Optimal Control of Uncertain Dynamical Systems with State-Dependent Switchings Using Interval Arithmetic

In this paper, interval arithmetic techniques for controller design of nonlinear dynamical systems with uncertainties are summarized. The main reason for the application of interval techniques in this context is the quantification of the influence of uncertainties and modeling errors. They result from neglecting nonlinear phenomena in the mathematical description of real-world systems. Furtherm...