The \(\alpha\)-embedded and \(A\)'s fuzzy decomposition theorems (Q1971961)
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scientific article; zbMATH DE number 1423478
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\alpha\)-embedded and \(A\)'s fuzzy decomposition theorems |
scientific article; zbMATH DE number 1423478 |
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The \(\alpha\)-embedded and \(A\)'s fuzzy decomposition theorems (English)
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2000
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The paper deals with decompositions of fuzzy sets based on the concept of \(\alpha\)-cuts. The attention is focused to several questions, namely if a fuzzy set can be decomposed into series of \(\alpha\)-cuts or into several sets derived from these \(\alpha\)-cuts and called their \(\alpha\)-embedded sets. The main results are formulated in several versions of fuzzy union-decomposition theorems and fuzzy intersection-decomposition theorems. The relation between these theorems is investigated as well.
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\(\alpha\)-cuts
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\(\alpha\)-embedded sets
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decompositions of fuzzy sets
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fuzzy union-decomposition
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fuzzy intersection-decomposition
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