In this paper, we first introduce the concept of quasi-coincidence of an intuitionistic fuzzy point within an intuitionistic fuzzy set. By using this new idea, we further introduce the notions of (∈, ∈ ∨ q)-intuitionistic fuzzy BCI-subalgebras of BCI-algebras and investigate some of their related properties. Some characterization theorems of these generalized intuitionistic fuzzy BCI-subalgebras are derived. Then we study the cartesian product of (∈, ∈ ∨ q)-intuitionistic fuzzy BCI-subalgebras. Finally, we introduce the homomorphism of intuitionistic fuzzy BCI-algebras, and prove that image and inverse image of an intuitionistic fuzzy set on a BCI-algebra should be an (∈, ∈ ∨ q)-intuitionistic fuzzy BCI-subalgebra on the basis of homomorphism of BCI-algebra.
AbdullahS., DavvazB. and AslamM., (α, β)-intuitionistic fuzzy ideals in hemirings, Computers and Mathematics with Applications62 (2011), 3077–3090.
2.
AbdullahS., AslamM. and HedayatiH., Interval valued (α, β)intuitionistic fuzzy ideals in hemirings, Journal of Intelligent and Fuzzy Systems26 (2014), 2873–2888.
3.
AbdullahS., AslamM. and HilaK., A new generalization of fuzzy biideals in semigroups and its applications in fuzzy finite state machines, Multiple Valued Logic and Soft Computing24 (2015), 599–623.
4.
AbdullahS. and AminN., Analysis of S-box image encryption based on generalized fuzzy soft expert set, Nonlinear Dynamics79 (2015), 1679–1692.
5.
AbdullahS. and AliA.F., Applications of N-structures in implicative filters of BE-algebras, Journal of Intelligent and Fuzzy Systems29(2) (2015), 517–524.
6.
AtanassovK., Intuitionistic fuzzy sets, Rep. No.1697/84. Central Technical Library, Bulgarian Academy Science, Sofia, (1983).
7.
AtanassovK., Intuitionistic Fuzzy Sets: Theory and Applications, Studies in fuzziness and soft computing, 35. Physica-Verlag, Heidelberg, 1999.
8.
BhowmikM., SenapatiT. and PalM., Intuitionistic L-fuzzy ideals of BG-algebras, Afrika Matematika25(3) (2014), 577–590.
9.
JanaC. and SenapatiT., Cubic G-subalgebras of G-algebras, Annals of Pure and Applied Mathematics10(1) (2015), 105–115.
10.
JanaC., SenapatiT., BhowmikM. and PalM., On intuitionistic fuzzy G-subalgebras of G-algebras, Fuzzy Information and Engineering7(2) (2015), 195–209.
11.
JanaC., PalM., SenapatiT. and BhowmikM., Atanassov’s intutionistic L-fuzzy G-subalgebras of G-algebras, The Journal of Fuzzy Mathematics23(2) (2015), 195–209.
12.
JanaC., SenapatiT. and PalM., Derivation, f-derivation and generalized derivation of KUS-algebras, Cogent Mathematics2 (2015), 1–12.
13.
JanaC. and PalM., Applications of new soft intersection set on groups, Annals of Fuzzy Mathematics and Informatics, in press.
14.
DudekW.A., ShabirM., Irfan AliM., (α, β)-fuzzy ideals of hemirings, Computers and Mathematics with Applications58 (2009), 310–321.
15.
ImaiY. and IsekiK., On axiom system of propositional calculi XIV, Proceedings of the Japan Academy42 (1966), 19–22.
16.
IśsekiK., An algebra related with a propositional calculus, Proceedings of the Japan Academy42 (1966), 26–29.
17.
JunY.B., On (α, β)-fuzzy subalgebras of BCK/BCI-algebras, Bull Korean Math Soc42(4) (2005), 703–711.
18.
JunY.B., Fuzzy subalgebras of type (α, β) in BCK/BCI-algebras, Kyungpook Math Journal47 (2007), 403–410.
19.
JunY.B. and KimK.H., Intuitionistic fuzzy ideals in BCK-algebras, Internat J Math Math Sci24(12) (2000), 839–849.
20.
LarimiM.A., On (∈, ∈ ∨ qk)-intuitionistic fuzzy ideals of hemirings, World Appl Sci21 (2013), 54–67.
21.
LiuY.L. and MengJ., Construction of quotient BCI(BCK)-algebra via a fuzzy ideal, Journal of Applied Mathematics and Computing10(1) (2002), 51–62.
22.
MaX., ZhanJ., DavvazB. and JunY.B., Some kinds of (∈, ∈ ∨ q)-interval-valued fuzzy ideals of BCI-algebras, Information Sciences178 (2008), 3738–3754.
23.
MaX., ZhanJ. and JunY.B., Some types of (∈, ∈ ∨ q)-interval-valued fuzzy ideals of BCI-algebras, Iranian Journal of Fuzzy Systems6 (2009), 53–63.
24.
MuraliV., Fuzzy points of equivalent fuzzy subsets, Information Sciences158 (2004), 277–288.
25.
NarayananA. and ManikantanT., (∈, ∈ ∨ q)-fuzzy subnearrings and (∈, ∈ ∨ q)-fuzzy ideals of nearrings, Journal of Applied Mathematics and Computing18 (2005), 419–430.
26.
PuP. and LiuY., Fuzzy topology I. Neighbourhood structures of a fuzzy point and Moore-Smith convergence, J Math Anal Appl76 (1980), 571–579.
27.
HongS.M., KimK.H. and JunY.B., Intuitionistic fuzzy subalgebras of BCK/BCI-algebras, Korean J Comput Appl Math8(1) (2001), 261–272.
28.
SenapatiT. and ShumK.P., Atanassov’s intuitionistic fuzzy binormed KU-ideals of a KU-algebra, Journal of Intelligent and Fuzzy Systems30 (2016), 1169–1180.
29.
SenapatiT., JanaC., BhowmikM. and PalM., L-fuzzy G-subalgebras of G-algebras, Journal of the Egyptian Mathematical Society23(2) (2015), 219–223.
30.
SenapatiT., BhowmikM. and PalM., Triangular norm based fuzzy BG-algebras, Afrika Matematika27(1) (2016), 187–199.
31.
SenapatiT., BhowmikM., PalM. and DavvazB., Fuzzy translations of fuzzy H-ideals in BCK/BCI-algebras, Journal of the Indonesian Mathematical Society21(1) (2015), 45–58.
32.
SenapatiT., BhowmikM. and PalM., Fuzzy dot structure of BG-algebras, Fuzzy Information and Engineering6(3) (2014), 315–329.
33.
SenapatiT., KimC.S., BhowmikM. and PalM., Cubic subalgebras and cubic closed ideals of B-algebras, Fuzzy Information and Engineering7(2) (2015), 129–149.
34.
SenapatiT., BhowmikM., PalM. and DavvazB., Atanassov’s intuitionistic fuzzy translations of Intuitionistic fuzzy subalgebras and ideals in BCK/BCI-algebras, Eurasian Mathematical Journal6(1) (2015), 96–114.
35.
SenapatiT., BhowmikM. and PalM., Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy H-ideals in BCK/BCI-algebras, Notes on Intuitionistic Fuzzy Sets19(1) (2013), 32–47.
36.
SenapatiT., BhowmikM. and PalM., Interval-valued intuitionistic fuzzy BG-subalgebras, The Journal of Fuzzy Mathematics20(3) (2012), 707–720.
37.
SenapatiT., Bipolar Fuzzy Structure of BG-subalgebras, The Journal of Fuzzy Mathematics23(1) (2015), 209–220.
38.
SenapatiT., Cubic Structure of BG-subalgebras of BG-algebras, The Journal of Fuzzy Mathematics24(1) (2016), 151–162.
39.
YuanX.H., LiH.X. and LeeE.S., On the definition of the intuitionistic fuzzy subgroups, Computers and Mathematics with Applications59 (2010), 3117–3129.
40.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
