An investigation on the $n$-fold IVRL-filters in triangle algebras

Abstract

The present study aimed to introduce n-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of n-fold (positive) implicative IVRL-extended filters and n-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the n-fold IVRL-extended filters, n-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.