The uncertainty theory solves problems with uncertain data. Often to perform arithmetic operations on uncertain data, the calculations on intervals are necessary. Interval arithmetic uses traditional mathematics in the calculations on intervals. There are many methods that solve the problems of uncertain data presented in the form of intervals, each of them can give in some cases different resu...

This paper generalizes the speciication of Basic Interval Arithmetic Sub-routines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend ...

A phenetic analysis of the 12 taxa or operational taxonomic units (OTUs) belonging to the three sections; Genea, Neobromus, and Nevskiella of the genus Bromus was performed. Unweighted pair-group method using arithmetic averages (UPGMA) and weighted pair-group method using arithmetic averages (WPGMA) clustering and factoriel method analyses were used to set the taxa apart. Forty-four characters...

Affine arithmetic is a well-known tool to reduce the wrapping effect of ordinary interval arithmetic. We discuss several improvements both in theory and in terms of practical implementation. In particular details of INTLAB’s affine arithmetic toolbox are presented. Computational examples demonstrate advantages and weaknesses of the approach.

A recent method by Shary for enclosing the solution set of a system of linear interval equations is derived in a new way. It is shown that the method converges to the fixed-point inverse, and that it has finite termination with probability 1.

Quantum-dot cellular automaton (QCA) is a novel nanotechnology with a very different computational method in compared with CMOS, whereas placement of electrons in cells indicates digital information. This nanotechnology with specifications such as fast speed, high parallel processing, small area, low power consumption and higher switching frequency becomes a promising candidate for CMOS tec...

As we advance into the new century, computers of the future will require techniques for arithmetic operations that take advantage of the modern technology and yield accurate results. Floating-point arithmetic has been in use for nearly forty years but is plagued with inaccuracies and limitations which necessitates introduction of a new concept in computer arithmetic called composite arithmetic....

This paper generalizes the speciication of Basic Interval Arithmetic Sub-routines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend ...

This paper generalizes the speci cation of Basic Interval Arithmetic Subroutines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend B...

Currently, nearly all methods for proving termination of imperative programs apply an unsound and incomplete abstraction by treating bitvectors and bitvector arithmetic as (unbounded) integers and integer arithmetic, respectively. This abstraction ignores the wraparound behavior caused by underand overflows in bitvector arithmetic operations. This is particularly problematic in the termination ...