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

Abstract

The conception of the bipolar complex fuzzy set (BCFS) is one of the fundamental and significant modifications of the fuzzy set (FS) to tackle the tricky and awkward information. BCFS has a rich and wider structure and has been utilized in various fields. In this article, we introduce the concept of bipolar complex fuzzy (BCF) subalgebras (BCFSAs), BCF ideals (BCFIs) of a BCK/BCI-algebra along with certain properties. Further, we investigate the relations between BCFSA and a BCFI and a necessary condition for BCFSA to be a BCFI. We also investigate characterizations of BCFI. Moreover, we introduce the notion of equivalence relations on the collection of all BCFIs of BCK/BCI algebra and the associated properties of equivalence relations.