Aggregation functions are key operators in fuzzy set theory. In this field, advances both from the theoretical and applied point of view have been a constant in the last decades. These operators have proven useful in responding to a growing need to handle large amounts of data and uncertainty and the associated challenges that arise. Families such as t-norms, t-conorms, uninorms, OWAs or Choquet integrals play an important role in fields such as decision making, image processing, fuzzy systems or fuzzy control.
On the other hand, fuzzy implication functions have experienced a boom in recent times with several books and state of the art devoted entirely to these operators. In addition to their theoretical importance in fuzzy set theory, there is a growing interest in the applications of these operators in data mining, approximate reasoning or computing with words, among other fields.
Fuzzy implication functions and aggregation functions are closely related since several families of aggregation functions have been successfully used in the generation of new families of fuzzy implication functions and functional equations where both operators are involved are common. Solving such functional equations provides operators with specific properties useful in certain applications.