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Full-Text Articles in Physical Sciences and Mathematics
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probability of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult -- crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we …
Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the important steps in deep learning is softmax, when we select one of the alternatives with a probability depending on its expected gain. A similar formula describes human decision making: somewhat surprisingly, when presented with several choices with different expected equivalent monetary gain, we do not just select the alternative with the largest gain; instead, we make a random choice, with probability decreasing with the gain -- so that it is possible that we will select second highest and even third highest value. Both formulas assume that we know the exact value of the expected gain for each …
For Quantum And Reversible Computing, Intervals Are More Appropriate Than General Sets, And Fuzzy Numbers Than General Fuzzy Sets, Oscar Galindo, Vladik Kreinovich
For Quantum And Reversible Computing, Intervals Are More Appropriate Than General Sets, And Fuzzy Numbers Than General Fuzzy Sets, Oscar Galindo, Vladik Kreinovich
Departmental Technical Reports (CS)
Need for faster and faster computing necessitates going down to quantum level -- which means involving quantum computing. One of the important features of quantum computing is that it is reversible. Reversibility is also important as a way to decrease processor heating and thus, enable us to place more computing units in the same volume. In this paper, we argue that from this viewpoint, interval uncertainty is more appropriate than the more general set uncertainty -- and, similarly, that fuzzy numbers (for which all alpha-cuts are intervals) are more appropriate than more general fuzzy sets. We also explain why intervals …