Unifunctions and Nullfunctions: A New Generalization of Overlap and Grouping Functions for Bipolar Modeling

Uninorms and nullnorms are important aggregation functions that exhibit bipolar behavior.However, their lack of continuity, particularly for uninorms, presents challenges in practical applications.Since associativity is often not essential, especially when aggregating only two values, we propose two new classes of functions: unifunctions and nullfunctions.These are inspired by overlap and grouping functions and aim to retain the structural advantages of uninorms and nullnorms while ensuring continuity.This paper introduces these new classes, explores their fundamental properties, and demonstrates their role in solving generalized Frank's equations under relaxed axioms.