From computation with guaranteed intervals to computation with confidence intervals: a new application of fuzzy techniques

Abstract

Traditional interval computations provide an estimate for the result y=f(x/sub 1/,...,x/sub n/) of data processing when we know intervals x/sub 1/,...,x/sub n/ that are guaranteed to contain the (unknown) actual values of the quantities x/sub 1/,...,x/sub n/. Often, in addition to these guaranteed intervals, we have confidence intervals for these quantities, i.e., intervals x/sub i/ that contain the corresponding values x/sub i/ with a certain probability. It is desirable, based on the confidence intervals for x/sub i/, to produce the resulting confidence interval for y. It turns out that the formulas for computing such resulting confidence interval are closely related with the formulas for processing fuzzy numbers by using Zadeh's extension principle. Thus, known algorithms for processing fuzzy data can be used to process confidence intervals as well.