journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2033 On the bipolar valued fuzzy RG-sub algebras Abrahem Showq Mohammed Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf, Iraq Zwain Basma M. Najaf Governorate Education Directorate, Ministry of Education, Najaf, Iraq Abbas Noor Dhahir Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf, Iraq 28 4-A 1067 1074 26 06 2025

This paper introduced the notions of bipolar-valued fuzzy RG-subalgebras on RG -RG-algebras and related properties. A number of theorems are posited backed by relevant examples. Afterwards, we presented a novel concept: the negative anti-fuzzy RG-subalgebra of RG-algebra. It is also studied how on SA-algebras, the bipolar valued fuzzy maps from their homomorphic images and inverse images become bipolar-valued fuzzy. Bipolar-valued fuzzy RG-subalgebras’ image and inverse image are defined. Let’s examine bipolar valued fuzzy by (BVF) rather.

 RG-algebra Fuzzy RG-sub algebra Bipolar valued fuzzy RG-sub algebras Upper level Lower level access open retracted no