Some types of generalized fuzzy \(n\)-fold filters in residuated lattices. (English) Zbl 1470.03020

Ma, Zhen Ming

Abstr. Appl. Anal. 2013, Article ID 736872, 8 p. (2013).

Summary: Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzy \(n\)-fold filters such as generalized fuzzy \(n\)-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.

MSC:

03G10	Logical aspects of lattices and related structures
03G25	Other algebras related to logic

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