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Joseph A Lorkowski, The University of Texas at El Paso
12-2010
Technical Report: UTEP-CS-10-34a
Published in Proceedings of the 30th Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2011, El Paso, Texas, March 18-20, 2011.
In many practical problems, we need to estimate the range of a given expression f(x1, ..., xn) when each input xi belongs to a known interval [xi] -- or when each input xi is described by a known fuzzy set. It is known that this problem is easy to solve when we have a Single Use Expression, i.e., an expression in which each variable xi occurs only once. In this paper, we show that for similarly defined Double Use Expressions, the corresponding range estimation problem is NP-hard. Similar problems are analyzed for the problem of solving linear systems under interval (and fuzzy) uncertainty.
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Technical Report: UTEP-CS-10-34a
Published in Proceedings of the 30th Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2011, El Paso, Texas, March 18-20, 2011.