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- W2602038294 abstract "Admissible orders have brought the structure of chains in the framework of interval-valued fuzzy sets. However, a deeper study of functions monotone with respect to admissible orders is still missing in the literature. In this work, we consider the construction of negations and strong negations on intervals with respect to admissible orders, in particular, for the Xu and Yager and lexicographical orders, as well as for those based on K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α</sub> operators. We introduce and discuss an approach to the construction of strong negations on intervals with respect to K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α,β</sub> orders based on an arbitrary couple of strong negations defined over the standard real interval [0, 1]. The introduced strong negations have a deep impact on all fields exploiting fuzzy methods dealing with intervals, allowing to introduce complements, dual aggregations, implications, entropies, etc." @default.
- W2602038294 created "2017-04-07" @default.
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- W2602038294 date "2018-04-01" @default.
- W2602038294 modified "2023-10-12" @default.
- W2602038294 title "Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory" @default.
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- W2602038294 doi "https://doi.org/10.1109/tfuzz.2017.2686372" @default.
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