Convexity invariance of fuzzy sets under the extension principles (Q1757918)
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scientific article; zbMATH DE number 6102742
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity invariance of fuzzy sets under the extension principles |
scientific article; zbMATH DE number 6102742 |
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Convexity invariance of fuzzy sets under the extension principles (English)
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7 November 2012
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Summary: We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse \(^\star\)-convex transformation, and also obtain some sufficient conditions for a mapping to be an \(^\star\)-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type-2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.
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