The supremum and infimum of the set of fuzzy numbers and its application (Q1363587)
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scientific article; zbMATH DE number 1046942
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The supremum and infimum of the set of fuzzy numbers and its application |
scientific article; zbMATH DE number 1046942 |
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The supremum and infimum of the set of fuzzy numbers and its application (English)
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10 August 1997
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A mapping \(u:R\to [0,1]\) is a fuzzy number, if it is normal (there exist \(x_0\in R\) such that \(u(x_0) =1)\), convex (i.e. all cuts \(\{x;u(x) \geq r\}\) are convex), upper semicontinuous, and if it has a compact support. The paper contains two main results. First, any bounded subset of the set of fuzzy numbers has a supremum and an infimum. Second, any continuous function from a compact interval to the set of fuzzy sets has a supremum and an infimum, of course, they need not be attained.
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fuzzy numbers
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supremum
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infimum
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continuous function
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