Abstract
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.
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Deschrijver, G., Kerre, E. (2008). Aggregation Operators in Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory. In: Bustince, H., Herrera, F., Montero, J. (eds) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Studies in Fuzziness and Soft Computing, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73723-0_10
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DOI: https://doi.org/10.1007/978-3-540-73723-0_10
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