The role of states in triangle algebras

In this paper, we enlarge the language of triangle algebra by adding a unary operation that describes properties of a state. These structure algebras are called state triangle algebra. The vital properties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and give some examples and properties of them are given. Using this concept, we define two types IVRL-extended $\sigma$-filters of a state triangle algebra.