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