International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/374 2020 2020 Department of Mathematics & Sciences, University of New Mexico, Gallup, NM 87301, USA Florentin Smarandache Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran Akbar Rezaei Department of Mathematics, Hanyang University, Seoul 04763, Korea Hee Sik Kim In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CI-algebras are not BE-algebras.   2020 2020 08 15 10.54216/IJNS.050101 https://www.americaspg.com/articleinfo/21/show/374