The role of states in triangle algebras

Abstract

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