Graded dominance and related graded properties of fuzzy connectives

Graded properties of binary and unary fuzzy connectives (valued in MTLΔMTLΔ-algebras) are studied, including graded monotony, a generalized Lipschitz property, commutativity, associativity, unit and null elements, and the dominance relation between fuzzy connectives. The apparatus of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool for easy derivation of graded theorems on the connectives.