The role of states in triangle algebras

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. Using this concept, we definetwo types IVRL-extended $sigma$-filters of a state trianglealgebra.