Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras

Abstract

————————————————————————————————- Abstract The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence relations on the family of all bipolar fuzzy ideals of a BCK/BCI-algebra is considered, and some related properties are discussed.