Implicators based on binary aggregation operators in interval-valued fuzzy set theory

In this paper we introduce aggregation operators on the lattice L*, which is the underlying lattice of both interval-valued fuzzy sets and intuitionistic fuzzy sets in the sense of Atanassov. We consider some particular classes of binary aggregation operators based on t-norms on the unit interval. We investigate the properties of the implicators generated by these classes. In particular, representations in terms of implicators on [0,1] are obtained, and the Smets-Magrez axioms are studied. We compare the results with those obtained for implicators generated by already known classes of t-norms on L*.