Aggregation operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory

Abstract

In this chapter we give an overview of some recent advances on aggregation operators on LI, where LI 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 LI, uninorms on LI and generators of uninorms on LI. We give the general definition and some special classes of aggregation operators on LI. Finally we discuss the generalization of Yager's OWA operators to interval-valued fuzzy set theory. © 2008 Springer-Verlag Berlin Heidelberg.