Let IIR be the set of closed and bounded intervals of real numbers. Arithmetic in IIR can be defined via the power set IPIR (the set of all subsets) of real numbers. If in case of division zero is not contained in the divisor arithmetic in IIR is an algebraically closed subset of the arithmetic in IPIR. Arithmetic in IPIR allows division by an interval that contains zero also. This results in c...

In this paper, we propose a new representation of numeric functions using a piecewise arithmetic expression. To represent a numeric function compactly, we partition the domain of the function into uniform segments, and transform the sub-function in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and obtain a piecewise arithmetic expre...

Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-th...

We propose the use of affine arithmetic in cell-mapping methods for the robust visualization of strange attractors and show that the resulting cellular approximations converge faster than those produced by cell-mapping methods based on classical interval arithmetic.

Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing w...