From Computation with Guaranteed Intervals to Computation with Confidence Intervals: A New Application of Fuzzy Techniques

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Hung T. Nguyen
Scott Ferson
Lev Ginzburg

Publication Date

5-2002

Comments

UTEP-CS-02-18.

Published in the Proceedings of the 21st International Conference of the North American Fuzzy Information Processing Society NAFIPS'2002, New Orleans, Louisiana, June 27-29, 2002, pp. 418-422.

Abstract

Traditional interval computations provide an estimate for the result y=f(x1,...,xn) of data processing when we know intervals X1,...,Xn that are guaranteed to contain the (unknown) actual values of the quantities x1,...,xn. Often, in addition to these guaranteed intervals, we have confidence intervals for these quantities, i.e., intervals Xi that contain the corresponding values xi with a certain probability. It is desirable, based on the confidence intervals for xi, 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.