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Generation of interval-valued fuzzy negations from Trillas’ theorem. The case of interval type-2 fuzzy sets. (English) Zbl 1371.03076

Magdalena, Luis (ed.) et al., Enric Trillas: a passion for fuzzy sets. A collection of recent works on fuzzy logic. Cham: Springer (ISBN 978-3-319-16234-8/hbk; 978-3-319-16235-5/ebook). Studies in Fuzziness and Soft Computing 322, 93-108 (2015).
In this work, the authors introduce a method for building interval-valued negations using the characterization theorem for strong negations which was proposed by E. Trillas [Stochastica 3, No. 1, 47–59 (1979; Zbl 0419.03035)]. They also show that interval type-2 fuzzy sets are a three-dimensional representation of interval-valued fuzzy sets and analyze the problems to build a complementation for such interval type-2 fuzzy sets. They finally propose a method to construct this complementation.
For the entire collection see [Zbl 1314.03008].

MSC:

03E72 Theory of fuzzy sets, etc.

Citations:

Zbl 0419.03035
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References:

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