Title :
Computations under time constraints: Algorithms developed for fuzzy computations can help
Author :
Villaverde, Karen ; Kosheleva, Olga ; Ceberio, Martine
Author_Institution :
Dept. of Comput. Sci., New Mexico State Univ., Las Cruces, NM, USA
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 Δa(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.
Keywords :
computational complexity; fuzzy set theory; number theory; Zadeh extension principle; algebraic product; binary representation; computational complexity; fuzzy computation; irrational real number; membership function; time constraint; Accuracy; Algorithm design and analysis; Approximation methods; Complexity theory; Data processing; Fast Fourier transforms;
Conference_Titel :
Fuzzy Information Processing Society (NAFIPS), 2011 Annual Meeting of the North American
Conference_Location :
El Paso, TX
Print_ISBN :
978-1-61284-968-3
Electronic_ISBN :
Pending
DOI :
10.1109/NAFIPS.2011.5752030