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Full-Text Articles in Computer Engineering
Combining Interval, Probabilistic, And Fuzzy Uncertainty: Foundations, Algorithms, Challenges -- An Overview, Vladik Kreinovich, David J. Berleant, Scott Ferson, Weldon A. Lodwick
Combining Interval, Probabilistic, And Fuzzy Uncertainty: Foundations, Algorithms, Challenges -- An Overview, Vladik Kreinovich, David J. Berleant, Scott Ferson, Weldon A. Lodwick
Departmental Technical Reports (CS)
Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval and probabilistic uncertainty. We provide an overview of related algorithms, results, and remaining open problems.
Towards Combining Probabilistic And Interval Uncertainty In Engineering Calculations: Algorithms For Computing Statistics Under Interval Uncertainty, And Their Computational Complexity, Vladik Kreinovich, Gang Xiang, Scott A. Starks, Luc Longpre, Martine Ceberio, Roberto Araiza, J. Beck, R. Kandathi, A. Nayak, R. Torres, J. Hajagos
Towards Combining Probabilistic And Interval Uncertainty In Engineering Calculations: Algorithms For Computing Statistics Under Interval Uncertainty, And Their Computational Complexity, Vladik Kreinovich, Gang Xiang, Scott A. Starks, Luc Longpre, Martine Ceberio, Roberto Araiza, J. Beck, R. Kandathi, A. Nayak, R. Torres, J. Hajagos
Departmental Technical Reports (CS)
In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.
In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known …