0555fcda-e64e-45c6-ae2d-2e08701d19d020210429095514171naun:naunmdt@crossref.orgMDT DepositInternational Journal of Pure Mathematics2313-057110.46300/91019http://www.naun.org/cms.action?id=6985292021292021810.46300/91019.2021.8https://www.naun.org/cms.action?id=23293GerimaTeferaWollo University, College of Natural Science, Department of Mathematics, Dessie, EthiopiaAbdiOliWollo University, College of Natural Science, Department of Mathematics, Dessie, EthiopiaIn this paper,the concepts of homomorphism in fuzzy BI-algebra is intro- duced, and also basic properties of homo- morphisms are investigated. The cartesian product in fuzzy ideals of BI-algebra is investigated with related prop- erties; The concepts of fuzzy topology on BI- algebra elaborated.429202142920212933https://www.naun.org/main/NAUN/puremath/2021/a062019-003(2021).pdf10.46300/91019.2021.8.3https://www.naun.org/main/NAUN/puremath/2021/a062019-003(2021).pdf10.1515/auom-2017-0014Arsham Boruman Saeid, Hee Sik Kim and Akbar Rezae, On BI- Algebras, An.st.Univ.Oridios constanta, vol. 25(1),2017,pp.177-194,Doi:10.1515—auom2017-0014. Boezooel,R.A.,Khosravishoar,S.,Implication algebras are equivalent to the dual implicative BCK-Algebras, Scientia Mathematicae Japonicae, on line ,e-2006, PP.371-373. Foster,D.H.,Fuzzy topological groups , J.Math.Anal.Appl.,67(1979),549-564. Gerima T., Fuzzy Ideals and Fuzzy filters in an implication algebra, On communication for publication,2020(9 page). Gerima T., and Abdi O., On Fuzzy BI-Algebra, On Communication ,2021(11 pages) 10.37418/amsj.10.3.6Gerima ,T., Endris,Y. and Fasil,G., Ideals and Filters on implication algebras, Advances in Mathematics:Scientific Journals, Vol.10(2021), No. 3, 1167-1174, ISSN : 1857- 8365(printed);1877-8435(electronic). Huang,Y.S., BCI-algebra, Science press, China,2006,ISBn:9787-03-015411-8. 10.9790/5728-1204055970Husein Hadi Abbas ,and Suad Abd Neamah, On the fuzzy implicative ideals of a BHalgebras, Vol. 12(4),(Aug.2016).PP.59-70, Doi:10.9790/5728-1204055970. Imai, Y., and Iseki, K., On axioms systems of propositional calculi, Xiv proc.Japan Academy,Vol. 42(1966), pp.19-22. Jun,Y.B.,Roh, E.H.,and Kim,H.S., Sci.math.Jpn.1/1998, On BH-algebras,pp.347- 354. Kandil,A., Saleh,S., and Myakout,M., Fuzzy topology on fuzzy sets; Regularity and separation axioms, American Academic and Scholarly Research Journals,vol. 4(2), March 2012. Karrar Dejaa Mohammed. A fuzzy λ− ideal of a BH-algebra, Journal of Kufa for Mathematics and Computer, Vol. 4 ,No.2,June ,2017, pp. 27- 33. 10.12732/ijpam.v115i2.2Khosravishoar,S., Fuzzy normal congruences and fuzzy coset relations on Groups,International Journal of pure and applied Mathematics ,Vol.115, No. 2,2017, pp.211-224, Doi: 10.12732/ijpam.v115i2.2. Neggers,J., and Kim,H.S., On Balgebras,Math.Vensik, Vol.54(2002),pp. 21-29. 10.12988/ams.2017.76191Sud Abdulaali Neamah, and Ayat Abdulaali Neamah, On the sub implicative ideals of a BH-algebra, Journal of University of Kerbala, vol.16,No. 1, 2018. Sunshin Ahn, Jungmiko, and Borumano Said, A., On Ideals of BI-algebras,J. Indones.math. Soc., vol. 25, No.(2019), pp.24-34. 10.1023/a:1021739030890Young Bae Jun, Roh,E,H.,Chinju, and Hee Sik Kim, Seoul , On fuzzy B-algebras, Czechoslovak Mathematical Journal, Vol. 52(127),2002,pp. 375-384. Zadeh,L.A. Fuzzy sets, Inform and Control,8(1965),338-353.