THE LATTICES OF L-FUZZY STATE FILTERS IN STATE RESIDUATED LATTICES

In the paper, we introduce L-fuzzy state filters in state residuated lattices and investigate their related properties, where L is a complete Heyting algebra. Moreover, we study the L-fuzzy state co-annihilator of an L-fuzzy set with respect to an L-fuzzy state filter. Finally, using the L-fuzzy state co-annihilator, we investigate lattice structures of the set of some types of L-fuzzy state filters in state residuated lattices. In particular, we prove that: (1) the set FSF[L] of all L-fuzzy state filters is a complete Heyting algebra; (2) the set SvFSF[L] of all stable state filters relative to an L-fuzzy set v is also a complete Heyting algebra; (3) the set I mu FSF[L] of all involutory L-fuzzy state filters relative to an L-fuzzy state filter it is a complete Boolean algebra. (C) 2020 Mathematical Institute Slovak Academy of Sciences