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Generalized Fuzzy Subalgebras And Fuzzy Ideals Of Bci-Algebras With Operators

Authors: Hu, Yuli; Shaoquan Sun;

Generalized Fuzzy Subalgebras And Fuzzy Ideals Of Bci-Algebras With Operators

Abstract

{"references": ["Y. Imai and K. Iseki, \"On axiom system of propositional calculus,\" Proc Aapan Academy, vol. 42, pp. 26-29,1966.", "K. Iseki, \"On BCI-algebras,\" Math. Sem. Notes, vol. 8, pp.125-130, 1980.", "O.G.Xi,\"Fuzzy BCK-algebras,\" Math Japon, vol. 36, pp. 935-942, 1991.", "J. Meng, Y.B. Jun and H.S. Kim, \"Fuzzy implicative ideals of BCK-Algebras,\" Fuzzy sets syst, vol. 89, pp. 243-248, 1997.", "W. X. Zheng, \"On BCI-algebras with operators and their isomorphism theorems,\" Journal of Qingdao University, vol. 6, pp. 17-22, 1993.", "Y.L.Liu and J. Meng, \"Fuzzy ideals in BCI-algebras,\" Fuzzy Sets and Systems, vol. 123, pp. 227-237, 2001.", "J. Meng, \"Fuzzy ideals of BCI-algebras,\" SEA Bull. Math, vol. 18, pp. 401- 405, 1994.", "Y. L. Liu, \"Characterizations of some classes of quotient BCI\u2013algebras\" Journal of Quan zhou Normal College (Natural Science Edition),vol. 20, pp. 16-20, 2002.", "Y.B. Jun, \"On (\u03b1,\u03b2)-fuzzy ideals of BCK/BCI-algebras,\" Sci. Math. Japon. vol. 60, pp. 613-617, 2004.\n[10]\tJ. 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.\n[11]\tZ.H. Liao and H. Gu, \"(\u2208,\u2208\u2228q(\u03bb,\u03bc))-fuzzy normal subgroup,\" Fuzzy Systems and Mathematics.vol.20, pp. 47-53,2006.\n[12]\tJ. Zhan, Y.B. Jun and B. Davvaz, \"On (\u2208,\u2208\u2228q)-Fuzzy ideals of BCI-algebras,\" Iranian Journal of Fuzzy Systems, vol. 6, pp. 81-94. 2009. \n[13]\tP.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.\n[14]\tY.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. \n[15]\tL.A. Zadeh, \"Fuzzy sets,\" Information and Control, vol. 8, pp. 338-353, 1965."]}

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

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

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