State filters on fuzzy structures with internal states
The aim of this paper is the study of some properties of the state filters of a state pseudo BL-algebra \(\left( A,\sigma \right) \) and also some properties of a state pseudo BL-algebra. By introducing the concepts of simple, semisimple and local state pseudo BL-algebra relative to its state filters set, we present some characterizations of a simple, semisimple and local state pseudo BL-algebras. Also, we adjust a result from universal algebra (Chinese remainder theorem) and, by introducing the concept of a primary state filter on a state BL-algebra, we present a characterization of a local state BL-algebra. We introduce the notion of extended state filter of a state filter associated to a subset of a state pseudo BL-algebra.
filter pseudo bl-algebra bl-algebra state operator state-filter