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Departmental Technical Reports (CS)

Computations under Time Constraints: Algorithms Developed for Fuzzy Computations Can Help

Karen Villaverde, New Mexico State University - Main CampusFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow

Publication Date

5-2011

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Technical Report: UTEP-CS-10-35b

Short version 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; detailed version to appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.

Abstract

In usual computers -- that use binary representation of real numbers -- an irrational real number (and even a rational number like 1.3 or 1.2) can only be computed with a finite accuracy. The more accuracy we need, the larger the computation time. It is therefore reasonable to characterize the complexity of computing a real number a by the accuracy D(t) that we can achieve in time t. Once we know this characteristic for two numbers a and b, how can we compute a similar characteristic for, e.g., c = a + b$? In this paper, we show that the problem of computing this characteristic can be reduced to the problem of computing the membership function for the sum -- when we use Zadeh's extension principle with algebraic product as the "and"-operation. Thus, known algorithms for computing this membership function can be used to describe computations under time constraints.

tr10-35.pdf (76 kB)
Original file: CS-UTEP-10-35
tr10-35a.pdf (81 kB)
Revised version: CS-UTEP-10-35a

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