Multiplication Distributivity of Proper and Improper Intervals

All About Generalized Interval Distributive Relations

The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus eecient solution of interval algebraic problems. This paper generalizes the distributive relations, known by now, on multiplication and addition of proper and improper intervals. A complete proof of the main results is presented, demonstrating an...

All About Generalized Interval Distributive Relations I Complete Proof of the Relations

The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus e cient solution of interval algebraic problems This paper generalizes the distributive relations known by now on multiplication and addition of proper and improper intervals A complete proof of the main results is presented demonstrating an orig...

A new algebraic and arithmetic framework for interval computations

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for mat...

Multiplication, distributivity and fuzzy-integral. III

On the Axiomatization of Interval Arithmetic

We investigate some abstract algebraic properties of the system of intervals with respect to the arithmetic operations and the relation inclusion and derive certain practical consequences from these properties. In particular, we discuss the use of improper intervals (in addition to proper ones) and of midpoint-radius presentation of intervals. This work is a theoretical introduction to interval...