{"title":"(\u2208,\u2208\u2228q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators","authors":"Yuli Hu, Shaoquan Sun ","volume":129,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":428,"pagesEnd":436,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008378","abstract":"The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-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. Zhan, Y.B. Jun and B. Davvaz, \u201cOn (\u2208,\u2208\u2228q)-Fuzzy ideals of BCI-algebras,\u201d Iranian Journal of Fuzzy Systems, vol. 6, pp. 81-94. 2009. \r\n[7]\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[8]\tY. L. Liu, \u201cCharacterizations of some classes of quotient BCI-algebras\u201d Journal of Quan zhou Normal College (Natural Science Edition),vol. 20, pp. 16-20, 2002.\r\n[9]\tJ.L, \u201cUniversal property of direct products of BCI-Algebra\u201d Journal of Jianghan University, vol. 18, pp. 36-38, 2001.\r\n[10]\tY.B. Jun, \u201cOn (\u03b1,\u03b2)-fuzzy ideals of BCK\/BCI-algebras,\u201d Sci. Math. Japon. vol. 60, pp. 613-617, 2004.\r\n[11]\tJ. Liu and S.Q. Sun, \u201cGeneralized fuzzy ideals of BCI-algebra,\u201d Journal of Qingdao University of Science and Technology (Natural Science Edition), vol. 32, pp. 211-215, 2011.\r\n[12]\tP.P. Ming and L.Y. Ming, \u201cNeighbourhood structure of a fuzzy point and Moore-Smith convergence,\u201d J. Math. Anal. Appl. vol. 76, pp. 571-599, 1980.\r\n[13]\tW.B. Pan, \u201cFuzzy ideals of sub-algebra and fuzzy H-ideals of sub-algebra,\u201d Degree of Qingdao University of Science and Technology, vol. 30, pp.468-470, 2009.\r\n[14]\tY.L.Hu and S.Q. Sun, \u201cfuzzy subalgebras and fuzzy ideals of BCI-algebras with operators, \u201d International Science Index, Mathematical and Computational Sciences, vol. 11, pp. 220-226, 2017.\r\n[15]\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 129, 2017"}