Generalized Atanassov's operators defined on lattice fuzzy multisets

In this paper the concept of an ordered weighted quasi-average operator (QOWA) on the one hand and that of an n-dimensional Atanassov's operator on the other, are extended from fuzzy multisets on [0, 1] to fuzzy multisets on any complete lattice endowed with a t-norm and a t-conorm. We show that, in the case of a distributive lattice, both operators provide particular cases of OWA operators defined on the lattice. In addition, a class of operators including Atanassov's ones is defined on fuzzy lattice multisets. This new approach allows us to build a kind of n-ary aggregation functions for complete lattices which generalizes OWA operators. (C) 2014 Elsevier Inc. All rights reserved.