Computations under time constraints: Algorithms developed for fuzzy computations can help

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 Δ_a(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.