Aggregation functions and contradictory information

The aim of this paper is to analyze the behavior of aggregation functions when the inputs are contradictory. This may be a useful criterion helping to choose the most appropriate function for solving a given problem. With that goal, bivariate aggregation functions are classified depending on the output they associate to contradictory couples of the form (x,N(x)), where N is a strong negation. The main properties of the newly defined classes are studied. Examples of functions in each class are provided, paying special attention to the most important families of aggregation functions, such as t-norms, copulas, symmetric sums, uninorms or nullnorms.