Results 1 to 10 of about 4,609 (163)
Beyond the Hausdorff metric in digital topology
Applied General Topology, 2022 Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or ...
Laurence Boxer
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The Hausdorff fuzzy quasi-metric
Fuzzy Sets and Systems, 2010 Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek's sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasi-pseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric.
Jesus Rodríguez-López, S Romaguera
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An Inequality for the Hausdorff-Metric of $\sigma$-Fields
Annals of Probability, 1986 The authors prove the following inequality, and then provide a number of consequent corollaries: Theorem: Let \({\mathcal A},{\mathcal B}\subset {\mathcal F}\) be \(\sigma\)-fields and let \(A_ i\in {\mathcal A}\), \(i\in I\), be disjoint sets. Then \[ \sum_{i\in I}{\tilde \rho}(A_ i,{\mathcal B})\leq 4\rho ({\mathcal A},{\mathcal B}) \] where \(\rho\)
D Landers, L Rogge
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The Hausdorff Metric of $\sigma$-Fields and the Value of Information [PDF]
Annals of Probability, 1993 The Hausdorff metric \(\delta^ 1({\mathcal F},{\mathcal G})\) of two sub- \(\sigma\)-fields \({\mathcal F},{\mathcal G}\subseteq\Sigma\) is defined with the help of the measure \(\mu(F\triangle G)\) of the symmetric difference of the sets \(F\in{\mathcal F}\), \(G\in{\mathcal G}\).
Timothy Van Zandt
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A unified framework for generalizing the Gromov-Hausdorff metric
Probability Surveys, 2023 61 pages. The first version of the paper is now split into two papers: The current one and `Metrization of the Gromov-Hausdorff (-Prokhorov) Topology for Boundedly-Compact Metric Spaces', arxiv:1901 ...
Ali Khezeli
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Hausdorff metric in the fuzzy environment
Ingeniería, 2016 Context: intuitively, the concept the set has been established as a collection of different elements, that is, a set is determined via the relationship of membership of an element of a universe as a whole. The situation, of course, is whether or does not
Laura Victoria Forero Vega +1 more
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The Hausdorff Algebra Fuzzy Distance and its Basic Properties [PDF]
Engineering and Technology Journal, 2021 In this article we recall the definition of algebra fuzzy metric space and its basic properties. In order to introduced the Hausdorff algebra fuzzy metric from fuzzy compact set to another fuzzy compact set we define the algebra fuzzy distance between ...
Zainab Khudhair, Jehad Kider
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The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
Mathematics, 2021 In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric.
Li Guan, Juan Wei, Hui Min, Junfei Zhang
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Fuzzy metric topology space and manifold [PDF]
Journal of Fuzzy Extension and Applications, 2023 This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces
Mahdi Mollaei Arani
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FPT-Algorithms for computing Gromov-Hausdorff and interleaving distances between trees
Journal of Computational Geometry, 2022 The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance
Elena Farahbakhsh Touli, Yusu Wang
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