State operators on generalizations of fuzzy structures
We enlarge the language of Rl-monoids, which are a non-commutative generalizations of both MV algebras and BL algebras, by adding a unary operation that describes algebraic properties of a state (= an analog of probability measures). The resulting algebras are called state Rl-monoids and state-morphism Rl-monoids. We present basic properties of such algebras. We describe subdirectly irreducible algebras, some generators of the varieties of state-morphism Rl-monoids, and an interplay between states and state operators. (C) 2011 Elsevier B.V. All rights reserved.
state operator state subdirectly irreducible algebras algebras of fuzzy logics residuated lattice state-morphism operator generators of varieties