Neutrosophic BCK-algebra and Ω-BCK-algebra

Saad H. Zail¹, Majid Mohammed Abed², Faisal AL-Sharqi^3,*

¹General Directorate of Education in Anbar, Ministry of Education, Ramadi, Anbar, Iraq

      ^2,3Department of Mathematics, Faculty of Education For Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq

Emails: SaadHaif50@gmail.com; Majid_math@uoanbar.edu.iq

Abstract

In this paper, we study neutrosophic of one important types of algebra namely BCK-algebra.  Some new results of a generalization of BCK-algebra (Ω-BCK-algebra) have been introduced. Several facts about neutrosophic Ω-BCK-algebra are presented such as neutrosophic of homomorphic image and neutrosophic of kernel homomorphism.  Finally, some definitions, examples, and other properties of neutrosophic BCK-algebra and neutrosophic Ω-BCK-algebra are given.

Keywords: Neutrosophic set; Neutrosophic algebra; BCK-algebra; BCI-algebra; Fuzzy set