| Title of paper:
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Additive generators in interval-valued and intuitionistic fuzzy set theory
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| Author(s):
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| Glad Deschrijver
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| Fuzziness and Uncertainty Modeling Research Unit, Department of Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium
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| Glad.Deschrijver@UGent.be
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| Published in:
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"Notes on IFS", Volume 12, 2006, Number 1, pages 30-37
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| Download:
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 PDF (126 Kb, File info)
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| Abstract:
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Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as [math]\displaystyle{ \mathcal{L} }[/math]-fuzzy sets w.r.t. a special lattice [math]\displaystyle{ \mathcal{L}^1 }[/math]. Deschrijver [2] introduced additive and multiplicative generators on [math]\displaystyle{ \mathcal{L}^I }[/math] based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on LI as far as possible independently of the addition. For some special additions we investigate which t-norms can be generated by continuous additive generators which are a natural extension of an additive generator on the unit interval.
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| Keywords:
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intuitionistic fuzzy set, interval-valued fuzzy set, additive generator, addition on [math]\displaystyle{ \mathcal{L}^I }[/math], representable.
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| AMS Classification:
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03E72
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| References:
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