.

 

(2) A new approach to evaluate interval functions

Overestimation is a major drawback in interval computation. Based on the inclusion monotone relation (7) and the physical/real means expressed by the interval function, a new approach to evaluate interval functions was proposed in this work.

Relation (7) is the fundamental property on which nearly all applications of interval arithmetic are based. It shows that it is possible to compute lower and upper bounds for the range over an interval by using only the bounds of the given interval without any further assumption.

Obviously, the true value of  is existing and unique.  means the range of  over . One of the original idea to introduce the interval function

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