Integrals of random fuzzy sets

DOI10.1007/BF02607061zbMath1137.28002MaRDI QIDQ882938

Volker Krätschmer

Publication date: 25 May 2007

Published in: Test (Search for Journal in Brave)

zbMATH Keywords

strong law of large numberscentral limit theoremrandom fuzzy setsAumann-integralBochner-integralPettis-integral

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Theory of fuzzy sets, etc. (03E72) Strong limit theorems (60F15) Fuzzy real analysis (26E50) Probability theory on linear topological spaces (60B11)

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Strong law of large numbers for t-normed arithmetics, Strong laws of large numbers for arrays of rowwise independent random compact sets and fuzzy random sets, Least-squares estimation in linear regression models with vague concepts, Some results on convergence and distributions of fuzzy random variables, Topological structure of (partially) hyperbolic sets with positive volume, Strong limit theorems for random sets and fuzzy random sets with slowly varying weights, Harmonizing two approaches to fuzzy random variables

Cites Work

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• Probability theory in fuzzy sample spaces
• Metric spaces of fuzzy sets
• \(L_p\) metrics for compact convex sets
• Integrals, conditional expectations, and martingales of multivalued functions
• The law of large numbers and the central limit theorem in Banach spaces
• The concept of a linguistic variable and its application to approximate reasoning. I
• Approximating integrably bounded fuzzy random variables in terms of the ``generalized Hausdorff metric
• On the variance of fuzzy random variables
• A generalized strong law of large numbers
• Fuzzy random variables, expectation, and martingales
• Constructive definitions of fuzzy random variables
• A strong law of large numbers for random upper semicontinuous functions under exchangeability conditions.
• Limit theorems for fuzzy-random variables
• Some complete metrics on spaces of fuzzy subsets
• Integrals of set-valued functions
• Pettis integral and measure theory
• Limit theorems for fuzzy random variables
• An elementary proof of the strong law of large numbers
• Fuzzy random variables
• A unified approach to fuzzy random variables
• On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data.