Residual implications and left-continuous t-norms which are ordinal sums of semigroups. (Q1428673)
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scientific article; zbMATH DE number 2062906
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Residual implications and left-continuous t-norms which are ordinal sums of semigroups. |
scientific article; zbMATH DE number 2062906 |
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Residual implications and left-continuous t-norms which are ordinal sums of semigroups. (English)
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29 March 2004
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In accordance with \textit{S. Jenei} [ibid. 126, 199--205 (2002; Zbl 0996.03508)], a left-continuous triangular norm with ordinal sum structure is represented as ordinal sum of left-continuous triangular subnorms. The authors prove that the residual implication is an ordinal sum of residual implications connected to the mentioned left-continuous triangular subnorms. Furthermore it is proved that a triangular subnorm, generated by a continuous additive generator \(r\), has its residual implication expressible by means of \(r\). Suitable examples are also given.
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additive generator
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ordinal sum
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residual implication
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t-norm
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t-subnorm
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