Computer Engineering Commons^™

Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

After Zadeh and Bellman explained how to optimize a function under fuzzy constraints, there have been many successful applications of this optimization. However, in many practical situations, it turns out to be more efficient to precisiate the objective function before performing optimization. In this paper, we provide a possible explanation for this empirical fact.

Computations Under Time Constraints: Algorithms Developed For Fuzzy Computations Can Help, Karen Villaverde, Olga Kosheleva, Martine Ceberio

Departmental Technical Reports (CS)

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 …

Estimating Probability Of Failure Of A Complex System Based On Partial Information About Subsystems And Components, With Potential Applications To Aircraft Maintenance, Christelle Jacob, Didier Dubois, Janette Cardoso, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Quantum Computations Techniques For Gauging Reliability Of Interval And Fuzzy Data, Luc Longpre, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

In traditional interval computations, we assume that the interval data corresponds to guaranteed interval bounds, and that fuzzy estimates provided by experts are correct. In practice, measuring instruments are not 100% reliable, and experts are not 100% reliable, we may have estimates which are "way off", intervals which do not contain the actual values at all. Usually, we know the percentage of such outlier un-reliable measurements. However, it is desirable to check that the reliability of the actual data is indeed within the given percentage. The problem of checking (gauging) this reliability is, in general, NP-hard; in reasonable cases, there …

Towards Neural-Based Understanding Of The Cauchy Deviate Method For Processing Interval And Fuzzy Uncertainty, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

One of the most efficient techniques for processing interval and fuzzy data is a Monte-Carlo type technique of Cauchy deviates that uses Cauchy distributions. This technique is mathematically valid, but somewhat counterintuitive. In this paper, following the ideas of Paul Werbos, we provide a natural neural network explanation for this technique.

Application-Motivated Combinations Of Fuzzy, Interval, And Probability Approaches, And Their Use In Geoinformatics, Bioinformatics, And Engineering, Vladik Kreinovich

Departmental Technical Reports (CS)

Most data processing techniques traditionally used in scientific and engineering practice are statistical. These techniques are based on the assumption that we know the probability distributions of measurement errors etc. In practice, often, we do not know the distributions, we only know the bound D on the measurement accuracy - hence, after the get the measurement result X, the only information that we have about the actual (unknown) value x of the measured quantity is that x belongs to the interval [X - D, X + D]. Techniques for data processing under such interval uncertainty are called interval computations; these …