{"title":"Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators","authors":"Yuli Hu, Shaoquan Sun","volume":126,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":235,"pagesEnd":242,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10007869","abstract":"The aim of this paper is to introduce the concepts of fuzzy subalgebras, fuzzy ideals and fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.","references":"[1]\tY. Imai and K. Iseki, \u201cOn axiom system of propositional calculus,\u201d Proc Aapan Academy, vol. 42, pp. 26-29, 1966.\r\n[2]\tK. Iseki, \u201cOn BCI-algebras,\u201d Math. Sem. Notes, vol. 8, pp.125-130, 1980.\r\n[3]\tO.G. Xi, \u201cFuzzy BCK-algebras,\u201d Math Japon, vol. 36, pp. 935-942, 1991.\r\n[4]\tY.B. Jun, S.M. Hong, J. Meng and X.L. Xin, \u201cCharacterizations of fuzzy positives implicative ideals in BCK-algebras\u201d, Math. Japon, vol. 40, pp.503-507, 1994.\r\n[5]\tY.B. Jun and E.H. Roh, \u201cFuzzy commutative ideals of BCK-algebras,\u201d Fuzzy Sets and Systems, vol. 64, pp. 401-405, 1994.\r\n[6]\tJ. Meng, Y.B. Jun and H.S. Kim, \u201cFuzzy implicative ideals of BCK-Algebras,\u201d Fuzzy sets syst, vol. 89, pp. 243-248, 1997.\r\n[7]\tY.B. Jun and J. Meng, \u201cFuzzy commutative ideals in BCI-algebras,\u201d Comm. Korean Math. Soc, vol. 9, pp. 19-25,1994.\r\n[8]\tW. X. Zheng, \u201cOn BCI-algebras with operators and their isomorphism theorems,\u201d Journal of Qingdao University, vol. 6, pp. 17-22, 1993.\r\n[9]\tY.L. Liu and J. Meng, \u201cFuzzy ideals in BCI-algebras,\u201d Fuzzy Sets and Systems, vol. 123, pp. 227-237, 2001.\r\n[10]\tJ. Meng, \u201cFuzzy ideals of BCI-algebras,\u201d S EA Bull. math, vol. 18, pp. 401- 405, 1994. \r\n[11]\tY. L. Liu, \u201cCharacterizations of some classes of quotient BCI\u2013algebras\u201d Journal of Quan zhou Normal College (Natural Science Edition),vol. 20, pp. 16-20, 2002.\r\n[12]\tJ.L, \u201cUniversal property of direct products of BCI-Algebra\u201d Journal of Jianghan University, vol. 18, pp. 36-38, 2001.\r\n[13]\tL.A. Zadeh, \u201cFuzzy sets,\u201d Information and Control, vol. 8, pp. 338-353, 1965.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 126, 2017"}