Abstract
In this paper, we introduce the notion of state monadic residuated lattices and study some of their related properties. Then we prove that the relationship between state monadic algebras of substructural fuzzy logics completely maintains the relationship between corresponding monadic algebras. Moreover, we introduce state monadic filters of state monadic residuated lattice, giving a state monadic filter generated by a nonempty subset of a residuated lattice, and obtain some characterizations of maximal and prime state monadic filters. Finally, we give some characterization of special kinds of state monadic residuated lattices, including simple, semisimple and local state monadic residuated lattices by state monadic filters.
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