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How To Propagate Interval (And Fuzzy) Uncertainty: Optimism-Pessimism Approach, Vinícius F. Wasques, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, inputs to a data processing algorithm are known with interval uncertainty, and we need to propagate this uncertainty through the algorithm, i.e., estimate the uncertainty of the result of data processing. Traditional interval computation techniques provide guaranteed estimates, but from the practical viewpoint, these bounds are too pessimistic: they take into account highly improbable worst-case situations when all the measurement and estimation errors happen to be strongly correlated. In this paper, we show that a natural idea of having more realistic estimates leads to the use of so-called interactive addition of intervals, techniques that has already …

When Is Propagation Of Interval And Fuzzy Uncertainty Feasible?, Vladik Kreinovich, Andrzej Pownuk, Olga Kosheleva, Aleksandra Belina

Departmental Technical Reports (CS)

In many engineering problems, to estimate the desired quantity, we process measurement results and expert estimates. Uncertainty in inputs leads to the uncertainty in the result of data processing. In this paper, we show how the existing feasible methods for propagating the corresponding interval and fuzzy uncertainty can be extended to new cases of potential practical importance.

Towards Decision Making Under General Uncertainty, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

There exist techniques for decision making under specific types of uncertainty, such as probabilistic, fuzzy, etc. Each of the corresponding ways of describing uncertainty has its advantages and limitations. As a result, new techniques for describing uncertainty appear all the time. Instead of trying to extend the existing decision making idea to each of these new techniques one by one, we attempt to develop a general approach that would cover all possible uncertainty techniques.

In Fuzzy Decision Making, General Fuzzy Sets Can Be Replaced By Fuzzy Numbers, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real decision situations, for each of the alternatives, we only have fuzzy information about the consequences of each action. This fuzzy information can be described by a fuzzy number, i.e., by a membership function with a single local maximum, or it can be described by a more complex fuzzy set, with several local maxima. We show that, from the viewpoint of decision making, it is sufficient to consider only fuzzy numbers. To be more precise, the decisions will be the same if we replace each original fuzzy set with the smallest fuzzy number of all fuzzy numbers of …

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 …