Discrete aggregation operators with annihilator

Mas et al. have investigated a special kind of commutative and associative aggregation operators with annihilator on the unit interval [0,1], which includes S-uninorms, S-nullnorms, T-uninorms, T-nullnorms, bi-uninorms and bi-nullnorms. This paper is devoted to extending this kind of operators from the unit interval [0,1] to a finite chain. A characterization of this kind of operators on a finite chain is given, including some examples. This class of operators can be viewed as a generalization of both uninorms and nullnorms on a finite chain.