New types of fuzzy ideals in BCK/BCI-algebras

A generalization of an (∈,∈∨q)-fuzzy ideal of a BCK/BCI-algebra is discussed. Characterizations of an (∈,∈∨qk)-fuzzy ideal and an (∈¯,∈¯∨qk¯)-fuzzy ideal are provided. Conditions for an (∈,∈∨qk)-fuzzy ideal (resp. (∈¯,∈¯∨qk¯)-fuzzy ideal) to be a fuzzy ideal are provided. Using the notion of a fuzzy ideal with thresholds, characterizations of a fuzzy ideal, an (∈,∈∨qk)-fuzzy ideal and an (∈¯,∈¯∨qk¯)-fuzzy ideal are discussed.