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Article

Zahiri, Saeide ; Borumand Saeid, Arsham
An investigation on the $n$-fold IVRL-filters in triangle algebras. (English). Mathematica Bohemica, vol. 145 (2020), issue 1, pp. 75-91
MSC: 03B50, 03B52, 08A30, 08A72 | MR 4088695 | Zbl 07217182 | DOI: 10.21136/MB.2019.0104-17
Keywords:
interval-valued structure; triangle algebra; interval valued residuated lattice filter; $n$-fold interval valued residuated lattice extended filter
Summary:
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.
References:
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