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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Aggregation Operators in Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory
verfasst von : Glad Deschrijver, Etienne Kerre
Erschienen in: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models
Verlag: Springer Berlin Heidelberg
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In this chapter we give an overview of some recent advances on aggregation operators on
L
I
, where
L
I
is the underlying lattice of interval-valued fuzzy set theory (which is equivalent to Atanassov’s intuitionistic fuzzy set theory). We discuss some special classes of t-norms on
L
I
and their properties. We show that the t-representable t-norms, which are constructed as a pair of t-norms on [0,1], are not the t-norms with the most interesting properties. We study additive generators of t-norms on
L
I
, uninorms on
L
I
and generators of uninorms on
L
I
. We give the general definition and some special classes of aggregation operators on
L
I
. Finally we discuss the generalization of Yager’s OWA operators to interval-valued fuzzy set theory.