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, 2017 Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and ...
Molchanov, Ilya, Ilya Molchanov
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Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables
SpringerBriefs in Applied Sciences and Technology, 2014Inés Couso, Luciano Sanchez
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SIAM Journal on Discrete Mathematics, 1994
For a random partition of an \(n\)-set the maximum part size and its multiplicity are investigated as \(n\to\infty\).
William M. Y. Goh, Eric Schmutz
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For a random partition of an \(n\)-set the maximum part size and its multiplicity are investigated as \(n\to\infty\).
William M. Y. Goh, Eric Schmutz
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RANDOMNESS IN THE HIGHER SETTING
The Journal of Symbolic Logic, 2015AbstractWe study the strengths of various notions of higher randomness: (i) strong ${\rm{\Pi }}_1^1$randomness is separated from ${\rm{\Pi }}_1^1$randomness; (ii) the hyperdegrees of ${\rm{\Pi }}_1^1$random reals are closed downwards (except for the trivial degree); (iii) the reals z in $NC{R_{{\rm{\Pi }}_1^1}}$ are precisely those satisfying $z \in ...
Chi Tat Chong, Liang Yu 0004
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The Distance of Random Permutation Set
Information Sciences, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luyuan Chen +2 more
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Theory of Probability & Its Applications, 1964
A Markov random set is a time-homogeneous random closed set on the half-line $t \geqq 0$, satisfying the Markov property of independence between the future and the past when the present is known. Such sets are introduced as a special class of Markov processes. They may be described by a non-increasing right-continuous positive function $g(x)$, $x > 0$,
Krylov, N. V., Yushkevich, A. A.
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A Markov random set is a time-homogeneous random closed set on the half-line $t \geqq 0$, satisfying the Markov property of independence between the future and the past when the present is known. Such sets are introduced as a special class of Markov processes. They may be described by a non-increasing right-continuous positive function $g(x)$, $x > 0$,
Krylov, N. V., Yushkevich, A. A.
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The random set and the cutting of random fuzzy sets
Fuzzy Sets and Systems, 1997The author presents several (rather obvious) results that relate a (possibly random) function \(A:X\to[0,1]\) (also called a fuzzy set), its random threshold \(A_\alpha= \{x\in X:A(x)\geq\alpha\}\) at random level \(\alpha\) (also called an \(\alpha\)-cut) and the coverage probabilities \(\mathbb{P}\{x\in A_\alpha\}\), \(x\in X\).
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2006
We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead 0001 +2 more
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We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead 0001 +2 more
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10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297), 2002
One of the main reasons why histograms are the most used density estimators is that they are easier to implement and interpret than other density estimators. Some people have already exploited the connection between probability theory and possibility theory or fuzzy sets to set up membership functions and to create fuzzy sets models. Two different ways
Javier Nunez-Garcia, Olaf Wolkenhauer
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One of the main reasons why histograms are the most used density estimators is that they are easier to implement and interpret than other density estimators. Some people have already exploited the connection between probability theory and possibility theory or fuzzy sets to set up membership functions and to create fuzzy sets models. Two different ways
Javier Nunez-Garcia, Olaf Wolkenhauer
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Graphs of Random Processes as Random Sets
Theory of Probability & Its Applications, 1987See the review in Zbl 0597.60015.
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