Abstract
Abstract In the paper, we introduce đ-fuzzy state filters in state residuated lattices and investigate their related properties, where đ is a complete Heyting algebra. Moreover, we study the đ-fuzzy state co-annihilator of an đ-fuzzy set with respect to an đ-fuzzy state filter. Finally, using the đ-fuzzy state co-annihilator, we investigate lattice structures of the set of some types of đ-fuzzy state filters in state residuated lattices. In particular, we prove that: (1) the set FSF[L] of all đ-fuzzy state filters is a complete Heyting algebra; (2) the set SÎœ FSF[L] of all stable state filters relative to an đ-fuzzy set Îœ is also a complete Heyting algebra; (3) the set IÎŒ FSF[L] of all involutory đ-fuzzy state filters relative to an đ-fuzzy state filter ÎŒ is a complete Boolean algebra.
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