##### Title: New types of bipolar fuzzy ideals of BCK-algebras

##### Pages: 859-875

##### Cite as:

G. Muhiuddin, D. Al-Kadi, A. Mahboob, K.P. Shum, New types of bipolar fuzzy ideals of BCK-algebras, Int. J. Anal. Appl., 18 (5) (2020), 859-875.#### Abstract

The notions of bipolar fuzzy closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are introduced, and related properties are investigated. Characterizations of a closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are given, and several properties are discussed. Finally, we prove that if T is an implicative BCK-algebra, then a fuzzy subset µ of T is a bipolar fuzzy ideal of T if and only if it is a bipolar fuzzy implicative ideal of T.

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