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

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.

[1]  Harrison M. Wadsworth.  Handbook of Statistical Methods for Engineers and Scientists , 1990 .

[2]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[3]  R. B. Kearfott,et al.  Applications of interval computations , 1996 .

[4]  Vladik Kreinovich,et al.  Towards Feasible Approach to Plan Checking under Probabilistic Uncertainty: Interval Methods , 2000, AAAI/IAAI.

[5]  Hung T. Nguyen,et al.  A First Course in Fuzzy Logic , 1996 .

[6]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[7]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[8]  S. Ferson,et al.  Hybrid arithmetic , 1995, Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society.