Wild t-norms (Q2714743)
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scientific article; zbMATH DE number 1607257
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wild t-norms |
scientific article; zbMATH DE number 1607257 |
Statements
2 July 2001
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triangular norm
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diagonal
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Cantor set
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Farey sequence
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Wild t-norms (English)
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The \textit{diagonal} of a triangular norm \(T\colon[0,1]^2\to[0,1]\) is the function \(D\colon[0,1]\to[0,1]\) defined by \(D(x)=T(x,x)\). G.~Krause has found a highly nontrivial example of a noncontinuous triangular norm with a continuous diagonal. Here the construction is clearly summarized. The paper is self-contained, possessing also an overview of the properties of Cantor sets and Farey sequence used in the construction. Consequences for the derivatives of diagonals of triangular norms are discussed in detail.
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