, Volume 25, Issue 2, pp 289-305
Date: 25 Oct 2012

Generalized fuzzy filters in non-commutative residuated lattices

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Non-commutative residuated lattices are a generalization of lattice-ordered onoids (briefly, R \(\ell \) -monoids). In this paper, based on the concepts of belongingness ‘ \(\in \) ’ and quasi-coincidence ‘q’, the theory of filters are developed, and to do this the concept of an \((\alpha ,\beta )\) -fuzzy filter with respect to a t-norm are introduced, where \(\alpha ,\beta \in \{\in ,q,\in \wedge q,\in \vee q\}\) . Some properties, characterizations and the connections among them are obtained, as well.