The operations and applications of fuzzy sets of type \(O\) (Q1278876)
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scientific article; zbMATH DE number 1255738
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The operations and applications of fuzzy sets of type \(O\) |
scientific article; zbMATH DE number 1255738 |
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The operations and applications of fuzzy sets of type \(O\) (English)
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21 September 1999
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Fuzzy sets of type \(O\) were introduced by \textit{Z.-G. Li} [Fuzzy Syst. Math. 1, 1-6 (1987) (Chinese)] as classes of membership functions \(A\colon U\to [0,1]\) connected with the partial order relation: \(x O y \Leftrightarrow A(x) > A(y), x, y \in U\). This paper examines binary operations on fuzzy sets preserving the order under selection of one of the equivalent membership scales. It is proved that the lattice operations are unique with respect to this property between triangular norms and conorms.
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fuzzy set
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fuzzy relation
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degree of membership
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triangular norm
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binary operations
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membership scales
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0.7646877765655518
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0.7573703527450562
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