174 Copyright © 2020, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 11 DOI: 10.4018/978-1-7998-0190-0.ch011 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 fnite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the fnite image, then every descending chain of H-ideals terminates at fnite step. 1. INTRODUCTION Zhang (1994) initiated the concept of bipolar fuzzy sets (BFSs) as a generalization of fuzzy sets (Zadeh, 1965). In fuzzy sets membership degree range is [0,1]. In a BFS membership degree range is increased from the interval [0,1] to the interval [-1,1]. The membership degree 0 means that elements are irrelevant to the corresponding property, the membership degrees on (0,1] indicate that elements somewhat satisfy the property and the membership degrees on [-1,0] indicate that elements somewhat satisfy the implicit counter-property. This domain has recently motivated new research in several directions (Akram, 2011, Dubois, 2008, Zadrozny & Kacprzyk, 2012, Zhang & Zhang, 2004). BCK-algebras and BCI-algebras are two important classes of logical algebras introduced by Imai & Iseki (1966). It is known that the class of BCK -algebra is a proper subclass of the class of BCI -algebras. Xi (1991) applied the concept of fuzzy sets to BCK-algebras. Jun (1993) applied it to BCI -algebras. Khalid and Ahmad (1999) introduced fuzzy H-ideals in BCI -algebras. Senapati et al. (2013, 2015) Bipolar Fuzzy Structure of H-Ideals in BCI-Algebras Tapan Senapati https://orcid.org/0000-0003-0399-7486 Southwest University, China Guiyun Chen Southwest University, China