We give a definition of a generalized state oper-ator (g-state operator) σ on a residuated lattice X and a g-state residuated lattice (X, σ ), by which the class of all g-state residuated lattices is proved to be a variety, and con- sider properties of g-state residuated lattices. We prove some fundamental results about them, such as characterizations of σ -filters, extended σ -filters, homomorphism theorems for g-state residuated lattices. Moreover, we show that every g- state residuated lattice is a subdirect product of subdirectly irreducible g-state residuated lattices.

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