| Title of paper:
|
(∈, ∈∨q)-Intuitionistic fuzzy prime ideals of BCK–algebras
|
| Author(s):
|
| S. R. Barbhuiya
|
| Department of Mathematics, Srikishan Sarda College, Hailakandi, Assam–788 151, India
|
| saidurbarbhuiya@gmail.com
|
| D. K. Basnet
|
| Department of Mathematical Sciences, Tezpur University, Tezpur, Assam–784 028, India
|
| dbasnet@tezu.ernet.in
|
|
| Published in:
|
"Notes on IFS", Volume 22, 2016, Number 1, pages 63-77
|
| Download:
|
 PDF (189 Kb, File info)
|
| Abstract:
|
In this paper, we introduced the concept of (∈, ∈∨q)-intuitionistic fuzzification of prime ideals in commutative BCK-algebras. We state and proved some theorems in (∈, ∈∨q)-intuitionistic fuzzy prime ideals in commutative BCK-algebras. Characterization of (∈, ∈∨q)-intuitionistic fuzzy prime ideal and conditions for (∈, ∈∨q)-intuitionistic fuzzy prime ideal to be an (∈, ∈)-intuitionistic fuzzy prime ideal are provided. Relation between (∈, ∈∨q)-intuitionistic fuzzy prime ideal and (∈∨q)-intuitionistic fuzzy level prime ideal were discussed.
|
| Keywords:
|
BCK-algebra, Prime ideal, Fuzzy prime ideal, (∈, ∈∨q)-Intuitionistic fuzzy prime ideal.
|
| AMS Classification:
|
06F35, 03E72, 03G25, 11R44.
|
| References:
|
- Abdullah, S. (2014) Intuitionistic fuzzy prime ideals of BCK-algebras, Annals of Fuzzy Mathematics and Informatics, 7(4), 661–668.
- Ahsan, J., Deeba, E. Y. & Thaheem, A. B. (1991) On prime ideal of BCK-algebras, Mathematica Japonica, 36, 875–882.
- Atanassov, K. T. (1986) Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, 87–96.
- Attallah, M. (2000) Completely Fuzzy Prime Ideals of distributed lattices, The Journal of Fuzzy Mathematics, 8(1), 153–156.
- Basnet, D. K. & Singh, L. B. (2011) (∈, ∈∨q)-fuzzy ideal of BG-algebra, International Journal of Algebra, 5(15), 703–708.
- Barbhuiya S. R. & Choudhury, K. D. (2014) (∈, ∈∨q)-Fuzzy ideal of d-algebra, International Journal of Mathematics Trends and Technology, 9(1), 16–26.
- Barbhuiya, S. R. (2015) (∈, ∈∨q)-Intuitionistic Fuzzy Ideals of BCK/BCI-algebra, Notes on Intuitionistic Fuzzy Sets, 21(1), 24–42.
- Bhakat, S. K. & Das, P. (1996) (∈, ∈∨q)-fuzzy subgroup, Fuzzy Sets and Systems, 80, 359–368.
- Bhakat, S. K. (1999) (2 _q)-level subset, Fuzzy Sets and Systems, 103, 529–533.
- Imai, Y. & Iseki, K. (1966) On Axiom systems of Propositional calculi XIV, Proc. Japan Academy, 42, 19-22.
- Iseki, K. (1966) An algebra related with a propositional calculus, Proc. Japan Academy, 42, 26–29.
- Iseki, K. (1975) On some ideals in BCK-algebras, Math. Seminar Notes, 3, 65–70.
- Koguep, B. B. N., Nkuimi, C. & Lele, C. (2008) On Fuzzy Ideals of Hyperlattice, International Journal of Algebra, 2(15), 739–750.
- Ming, P. P. & Ming, L. Y. (1980) Fuzzy topology.I., Neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Maths. Anal. Appl., 76, 571–599.
- Murali, V. (2004) Fuzzy points of equivalent fuzzy subsets, Information Sciences, 158, 277–288.
- Swamy, U. M. & Raju, D. V. (1998) Fuzzy ideals and Congruences of lattices, Fuzzy Sets and Systems, 95, 249–253.
- Jun, Y. B. & Xin, X. L. (2001) Involutory and invertible fuzzy BCK-algebras, Fuzzy Sets and Systems, 117, 463–469.
- Jun, Y. B. & Xin, X. L. (2001) Fuzzy prime ideals and invertible fuzzy ideals in BCKalgebras, Fuzzy Sets and Systems, 117, 471–476.
- Jun, Y. B. (2004) On (α, β)-Fuzzy ideals of BCK/BCI-Algebras, Scientiae Mathematicae Japonicae, online, 101–105.
- Zadeh, L. A. (1965) Fuzzy sets, Information and Control, 8, 338–353.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
