Characterizations of n-fold Filters in Triangle Algebras
Saeide Zahiri and Arsham Borumand Saeid
The aim of this paper is to develop the filter theory of triangle algebras. First, we define some particular types of n-fold interval valued residuated lattice extended filters (IVRL-extended filters). Based on which some new results are found on n-fold IVRL-extended (obstinate, fantastic, integral, easy) filter of triangle algebras. The relationships between these types of n-fold IVRL-filters defined in this paper are investigated. Accordingly, we prove that every n-fold IVRL-extended obstinate filter is an n-fold IVRL-extended fantastic and integral filter. Some conditions under which n-fold IVRL filters are n-fold IVRL-extended obstinate filter are considered. Finally, a schematic summary of relations among all n-fold IVRL-extended filters that we will elaborate in this paper are given.
Keywords: Non-classical logics, triangle algebra, IVRL-filter, n-fold IVRL-extended
AMS Classification 2010: 08A72, 08A30, 03B50, 03B52.