Generalizations of ( ? , ? ? q ) -fuzzy subalgebras in BCK/BCI-algebras
More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy set is considered, and generalizations of results in the papers [Y. B. Jun, On (?,?) ( ? , ? ) -fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc. 42 (4) (2005) 703711; Y. B. Jun, Fuzzy subalgebras of type (?,?) ( ? , ? ) in BCK/BCI-algebras, Kyungpook Math. J. 47 (2007) 403410] are discussed. The notions of ( ? , q k ) -fuzzy subalgebras and ( ? , ? ? q k ) -fuzzy subalgebras in a BCK/BCI-algebra X X are introduced, and several properties are investigated. Characterizations of ( ? , ? ? q k ) -fuzzy subalgebra in a BCK/BCI-algebra X X are discussed.
( ? ( ? bck/bci-algebra q k ) ? ? q k ) q k ) -fuzzy subalgebra ( ? q k ) ( ? ? ? q k ) -fuzzy subalgebra ( ? ? ? q k ) ( ? ( ? ? q k ) -level subalgebra ( ? ? q k ) ( ? ? q k ) ( ? ? q k )