The role of states in triangle algebras

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran.

2 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran


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