Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30121
(∈,∈∨q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

Authors: Yuli Hu, Shaoquan Sun

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.

Keywords: BCI-algebras with operators, (∈, ∈∨q)-fuzzy subalgebras, (∈, ∈∨q)-fuzzy ideals, (∈, ∈∨q)-fuzzy quotient algebras.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1314901

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 395

References:


[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] Y.B. Jun, S.M. Hong, J. Meng and X.L. Xin, “Characterizations of fuzzy positives implicative ideals in BCK-algebras”, Math. Japon, vol. 40, pp. 503-507, 1994.
[5] Y.B. Jun and E.H. Roh, “Fuzzy commutative ideals of BCK-algebras,” Fuzzy Sets and Systems, vol. 64, pp. 401-405, 1994.
[6] 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.
[7] W. X. Zheng, “On BCI-algebras with operators and their isomorphism theorems,” Journal of Qingdao University, vol. 6, pp. 17-22, 1993.
[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] J.L, “Universal property of direct products of BCI-Algebra” Journal of Jianghan University, vol. 18, pp. 36-38, 2001.
[10] Y.B. Jun, “On (α,β)-fuzzy ideals of BCK/BCI-algebras,” Sci. Math. Japon. vol. 60, pp. 613-617, 2004.
[11] 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.
[12] 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.
[13] W.B. Pan, “Fuzzy ideals of sub-algebra and fuzzy H-ideals of sub-algebra,” Degree of Qingdao University of Science and Technology, vol. 30, pp.468-470, 2009.
[14] Y.L.Hu and S.Q. Sun, “fuzzy subalgebras and fuzzy ideals of BCI-algebras with operators, ” International Science Index, Mathematical and Computational Sciences, vol. 11, pp. 220-226, 2017.
[15] L.A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338-353, 1965.