MONADIC EQ-ALGEBRAS

The chief aim of this paper is to study monadic EQ-algebras. First, we reveal the concept of monadic EQ-algebras, that is, EQ-algebras equipped with universal and existential quantifiers. Then, we testify certain basic properties of monadic EQ-algebras, and we obtain that some elements of monadic EQ-algebra can constitute its subalgebras under certain conditions. Finally, we introduce monadic filters(prefilters) of monadic EQ-algebras. We show that there is a one-to-one correspondence between monadic filter and monadic congruence on good monadic EQ-algebras. These bear fruits provide a more universal algebraic foundations for dealing with uncertain information.