A Generalization of (Implicative) (E,E vq)-Fuzzy Ideals of Pseudo-MV Algebras
Using a generalized version of the notion of quasi-coincidence of a fuzzy point, a generalization of (implicative) (∈,∈ ∨q)-fuzzy ideal, called (implicative) (∈,∈ ∨qk)-fuzzy ideal, in a pseudo-MV algebra is introduced. Also (implicative) (∈,∈ ∨qk)-fuzzy ideals are characterized in different ways. Specially, it is proved that, under certain conditions, an implicative (∈,∈ ∨qk)-fuzzy ideal can be expressed as the union of two implicative (∈,∈ ∨qk)-fuzzy ideals. Finally, a generalization of (implicative) implication-based fuzzy ideals is introduced and studied.
Keywords: Pseudo-MV algebra, quasi-coincidence, (implicative) implicationbased fuzzy ideal
2000 Mathematics Subject Classification: 08A72, 06D35