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Confidence Intervals for Stochastic Arithmetic [PDF]
ACM Transactions on Mathematical Software, 2021 Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes.
Sohier, Devan +5 more
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Automatic differentiation of uncertainties: an interval computational differentiation for first and higher derivatives with implementation [PDF]
PeerJ Computer Science, 2023 Acquiring reliable knowledge amidst uncertainty is a topical issue of modern science. Interval mathematics has proved to be of central importance in coping with uncertainty and imprecision.
Hend Dawood, Nefertiti Megahed
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Using interval arithmetic for providing a MADM approach [PDF]
Journal of Fuzzy Extension and Applications, 2020 The VIKOR method was developed for Multi-Criteria Decision Making (MCDM). It determines the compromise ranking list and the compromise solution obtained with the initial weights.
Hossein Jafari, Mohammad Ehsanifar
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Applied Sciences, 2022 In scientific journals, it is increasingly common to find articles presenting methods for solving problems not based on idealistic mathematical models containing perfectly accurate coefficient values that cannot be obtained in practice, but on models in ...
Andrzej Piegat, Marcin Pluciński
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Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers
Mathematics, 2021 Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithmetic ...
Qingsong Mao, Huan Huang
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International Journal of Applied Mathematics and Computer Science, 2023 The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in ...
Piegat Andrzej, Pluciński Marcin
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Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values [PDF]
International Journal of Computational Intelligence Systems, 2015 Moore's interval arithmetic always provides the same results of arithmetic operations, e.g. [1, 3]+ [5, 9]= [6, 12]. But in real life problems, the operation result can be different, e.g. equal to [4, 7].
Andrzej Piegat, Marcin Plucinski
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Granular computational homogenisation of composite structures with imprecise parameters
Archives of Mechanics, 2023 The paper presents the formulation of a granular computational homogenisation problem and the proposition of a method to solve it, which enables multiscale analysis of materials with uncertain microstructure parameters.
W. Beluch, M. Hatłas, J. Ptaszny
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Hardware Support for Interval Arithmetic [PDF]
Reliable Computing, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kirchner, Reinhard, Kulisch, Ulrich W.
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A Decomposition Approach to Type 2 Interval Arithmetic
International Journal of Applied Mathematics and Computer Science, 2020 The classic interval has precise borders A=[a_,a¯]A = \left[ {\underline{a},\bar a} \right]. Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have ...
Piegat Andrzej, Dobryakova Larisa
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