Bipolar Fuzzy Structure of H-Ideals in BCI-Algebras

Abstract

In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their natures are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy H-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy H-ideal are provided. Some characterization theorems of bipolar fuzzy H-ideals are established. A bipolar fuzzy H-ideal is established by using a finite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the finite image, then every descending chain of H-ideals terminates at finite step.