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On Upper Functions for Stochastic Approximation Procedures
Theory of Probability & Its Applications, 1984Translation from Teor. Veroyatn. Primen. 28, No.4, 769-775 (Russian) (1983; Zbl 0536.62064).
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The lower and upper approximations and homomorphisms between lower approximations in quotient groups
Journal of Intelligent & Fuzzy Systems, 2017Rough sets are an emerging mathematical tool in the field of data analysis. The relation between rough sets and algebraic systems (groups, rings and modules etc.) has already been identified. In this paper we studied the lower and upper approximations of a rough set in a quotient group.
Waqas Mahmood +2 more
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On Upper Bounds for Variances in Stochastic Approximation
SIAM Journal on Applied Mathematics, 1973Sufficient conditions for convergence of both the Robbins–Monro and Kiefer–Wolfowitz procedures are investigated, with emphasis on the variances and second moments of observation. The subsequent choice of design is compared with previous results.
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The characterizations of upper approximation operators based on coverings
Soft Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pei Wang, Qingguo Li
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Upper and lower bounds for approximation in the gap metric
IEEE Transactions on Automatic Control, 1993Summary: This note establishes upper and lower bounds for the closest approximant of degree ...
Tryphon T. Georgiou, Malcolm C. Smith
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Rough data-deduction based on the upper approximation
Information Sciences, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuo Yan, Lin Yan 0002, Jinzhao Wu
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Approximating the Rainbow – Better Lower and Upper Bounds
2012In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph where each edge is coloured with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e.
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The Axiomatization of the Rough Set Upper Approximation Operations
Fundamenta Informaticae, 2006The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called, respectively, the lower and the upper approximation. There are at least two methods for the development of this theory, the constructive and the axiomatic approaches.
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On the approximation of Hausdorff upper semi-continuous correspondences
Mathematische Zeitschrift, 1988The author establishes several approximation theorems for Hausdorff upper semi-continuous correspondences having for range a locally convex space. The main results show that under certain hypotheses such correspondences can be approximated from above by correspondences of the form \(\sum _{j\in J}\beta _ jA_ j\) where \((\beta _ j)_{j\in J}\) is a ...
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