Commutative Weak t-Norm and Non-associative Residuated Lattices

Based on weak t-norm introducing by J.C. Fodor from fuzzy set theory and strict preference relation, a new notion of non-associative residuated lattice is introduced. The following result is proved: from a commutative weak t-norm, a non-associative residuated lattice can be constructed. Moreover, the relationship among non-associative residuated lattices, implication lattices and lattice-valued interval sets are investigated.