The notions of a bipolar fuzzy regularity, a bipolar fuzzy regular subalgebra, a bipolar fuzzy filter, and a bipolar fuzzy closed quasi filter in BCH-algebras are introduced, and several properties are investigated. A characterization of a bipolar fuzzy filter is provided. Mathematics Subject Classification: 06F35, 03G25, 08A72

The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

We introduce the notion of bipolar fuzzy soft Lie subalgebras and investigate some of their properties. We also introduce the concept of an (∈,∈ ∨q)-bipolar fuzzy (soft) Lie subalgebra and present some of its properties.