First-Order Mathematical Fuzzy Logic with Hedges

In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This is based on the fact that, in the real world, many hedges can be used simultaneously, and some hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge may or may not have a dual one. We expand two axiomatizations for propositional mathematical fuzzy logic with many hedges to the first-order level and prove a number of completeness results for the resulting logics. We also consider logics with many hedges based on -core fuzzy logics.