On a class of generated triangular norms and their isomorphisms (Q969573)
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scientific article; zbMATH DE number 5705392
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a class of generated triangular norms and their isomorphisms |
scientific article; zbMATH DE number 5705392 |
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On a class of generated triangular norms and their isomorphisms (English)
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7 May 2010
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Let \(f_1\) and \(f_2\) be two strictly decreasing additive generators of border-continuous triangular norms \(T_1\) and \(T_2\), respectively. Necessary and sufficient conditions on \(f_1,f_2\) are given in order to ensure that the semigroups \(([0,1],T_1)\) and \(([0,1],T_2)\) are isomorphic. The conditions are expressed in terms of the ranges of the generators. Analogous results for triangular conorms are given.
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additive generator
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associative law
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Cauchy functional equation
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commutative totally ordered semigroup
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isomorphism
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triangular norm
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