On maximal filters in triangle algebras
Saeide Zahiri, Arsham Borumand Saeid, Esfandiar Eslami · Journal of Intelligent & Fuzzy Systems · 2015
In this paper, we define two types of maximal filters in triangle algebras. The concepts of the radical of a triangle algebra and radical of an interval valued residuated lattice-filter (IVRL-filter) in triangle algebras are introduced. Some characterizations of the radical of an IVRL-filter are given. The notion of IVRL-extended semi maximal filter in triangle algebras also introduced. We investigate the relations between this notion and other types of IVRL-filters in triangle algebras. Special elements such as dense elements and double complemented elements in triangle algebras are defined. Properties of the collections of these elements as well as properties of IVRL-filters in triangle algebras are studies.