A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread
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Publication:845309
DOI10.1016/j.ins.2009.06.023zbMath1181.62016OpenAlexW2025174402MaRDI QIDQ845309
Wolfgang Trutschnig, Gil González-Rodríguez, Ana Colubi, María Ángeles Gil Álvarez
Publication date: 28 January 2010
Published in: Information Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ins.2009.06.023
fuzzy setsdistancesupport functionsimprecise data analysisconvex compact setsgeneralized mid and spread
Statistical distribution theory (62E99) Fuzziness in connection with statistical distributions (62E86)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Least squares fitting of an affine function and strength of association for interval-valued data
- Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data
- Is there a need for fuzzy logic?
- Simulation of fuzzy random variables
- Bootstrap approach to the multi-sample test of means with imprecise data
- Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy- and real-valued data
- \(L_p\) metrics for compact convex sets
- The concept of a linguistic variable and its application to approximate reasoning. I
- Estimating the expected value of fuzzy random variables in the stratified random sampling from finite populations
- Some complete metrics on spaces of fuzzy subsets
- Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients
- Toward a generalized theory of uncertainty (GTU) -- an outline
- Limit theorems for fuzzy random variables
- Measure and integration theory
- A generalized real-valued measure of the inequality associated with a fuzzy random variable
- On the formalization of fuzzy random variables
- Two-sample hypothesis tests of means of a fuzzy random variable
- Special issue: Fuzzy random variables
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