A Review of the Relationships between Aggregation, Implication and Negation Functions

Aggregation functions, on one hand, and implication functions, on the other, play different although important roles in the field of fuzzy logic. Both have been intensively investigated in the last years, revealing the tide relationship that exists between them. The present work reviews the most relevant aspects of this relation, which most of the times also involves negation functions. In addition to the well-known use of aggregation and negation functions to build and to characterize implication functions, we analyze how new families of aggregation functions and negation functions can be obtained from implications, and we recall the main equations and inequations involving these three classes of functions.