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Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

Authors: Yuli Hu, Shaoquan Sun


The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

Digital Object Identifier (DOI):

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[1] Y. Imai and K. Iseki, “On axiom system of propositional calculus,” Proc Aapan Academy, vol. 42, pp. 26-29,1966.
[2] K. Iseki, “On BCI-algebras,” Math. Sem. Notes, vol. 8, pp.125-130, 1980.
[3] O.G.Xi,“Fuzzy BCK-algebras,” Math Japon, vol. 36, pp. 935-942, 1991.
[4] J. Meng, Y.B. Jun and H.S. Kim, “Fuzzy implicative ideals of BCK-Algebras,” Fuzzy sets syst, vol. 89, pp. 243-248, 1997.
[5] W. X. Zheng, “On BCI-algebras with operators and their isomorphism theorems,” Journal of Qingdao University, vol. 6, pp. 17-22, 1993.
[6] Y.L.Liu and J. Meng, “Fuzzy ideals in BCI-algebras,” Fuzzy Sets and Systems, vol. 123, pp. 227-237, 2001.
[7] J. Meng, “Fuzzy ideals of BCI-algebras,” SEA Bull. Math, vol. 18, pp. 401- 405, 1994.
[8] Y. L. Liu, “Characterizations of some classes of quotient BCI–algebras” Journal of Quan zhou Normal College (Natural Science Edition),vol. 20, pp. 16-20, 2002.
[9] Y.B. Jun, “On (α,β)-fuzzy ideals of BCK/BCI-algebras,” Sci. Math. Japon. vol. 60, pp. 613-617, 2004.
[10] J. Liu and S.Q. Sun, “Generalized fuzzy ideals of BCI-algebra,” Journal of Qingdao University of Science and Technology (Natural Science Edition), vol. 32, pp. 211-215, 2011.
[11] Z.H. Liao and H. Gu, “(∈,∈∨q(λ,μ))-fuzzy normal subgroup,” Fuzzy Systems and Mathematics.vol.20, pp. 47-53,2006.
[12] J. Zhan, Y.B. Jun and B. Davvaz, “On (∈,∈∨q)-Fuzzy ideals of BCI-algebras,” Iranian Journal of Fuzzy Systems, vol. 6, pp. 81-94. 2009.
[13] P.P. Ming and L.Y. Ming, “Neighbourhood structure of a fuzzy point and Moore-Smith convergence,” J. Math. Anal. Appl. vol. 76, pp. 571-599, 1980.
[14] Y.L.Hu and S.Q. Sun, “fuzzy subalgebras and fuzzy ideals of BCI-algebras with operators,” International Science Index, Mathematical and Computational Science, vol. 6, pp. 220-226. 2017.
[15] L.A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338-353, 1965.