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Issue:Additive generators in interval-valued and intuitionistic fuzzy set theory

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Title of paper: Additive generators in interval-valued and intuitionistic fuzzy set theory
Author(s):
Glad Deschrijver
Fuzziness and Uncertainty Modeling Research Unit, Department of Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium
Glad.Deschrijver@UGent.be
Published in: "Notes on IFS", Volume 12, 2006, Number 1, pages 30-37
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Abstract: 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.
Keywords: intuitionistic fuzzy set, interval-valued fuzzy set, additive generator, addition on [math]\displaystyle{ \mathcal{L}^I }[/math], representable.
AMS Classification: 03E72
References:
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  2. G. Deschrijver, Additive and multiplicative generators in interval-valued fuzzy set theory, submitted.
  3. G. Deschrijver, Algebraic operators in interval-valued fuzzy set theory, submitted.
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