IJPAM: Volume 117, No. 3 (2017)

Title

ANTI FUZZY IDEALS OF B-ALGEBRAS

Authors

Deena Al-Kadi
Department of Mathematics and Statistic
Taif University
Al-Hawiya, P.O. Box 888, Taif 21974, Taif, SAUDI ARABIA

Abstract

In this paper we introduce the notion of anti fuzzy ideals of B-algebras and we give characterizations of it using the notion of lower level subset. We also study the properties of anti fuzzy ideals under homomorphism of B-algebras. We consider the cartesian product of anti fuzzy ideals and investigate some properties.

History

Received: 2017-05-22
Revised: 2017-07-29
Published: January 15, 2018

AMS Classification, Key Words

AMS Subject Classification: 06F35, 03G25
Key Words and Phrases: B-algebras, fuzzy ideal, anti fuzzy ideal

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
S. S. Ahn and K. Bang, On fuzzy subalgebras in B-algebras, Commun. Korean Math. Soc., 18, No. 3 (2003), 429-438, doi: https://doi.org/10.4134/CKMS.2003.18.3.429.

2
N. O. Al-Shehri, Anti Fuzzy Implicative Ideals in BCK-Algebras, Punjab Univ. J. Math., 43, (2011), 85-91.

3
J. R. Cho and H. S. Kim, On B-algebras and quasigroups, Quasigroups Related Systems, 8 (2001), 1-6.

4
O. R. El-Gendy, Anti-fuzzy BRK-Ideal of BRK-Algebra, British Journal of Mathematics and Computer Science, 10, No. 6 (2015), 1-9, doi: https://doi.org/10.9734/BJMCS/2015/19309.

5
K. Iséki, An algebra related with a propositional calculus, Proceedings of the Japan Academy, 42, No. 1 (1966), 26-29 , doi: https://doi.org/10.3792/pja/1195522171.

6
Y. Imai, and K. Iséki, On axiom systems of propositional calculi. XIV, Proceedings of the Japan Academy, 42, No. 1 (1966), 19-22, doi: https://doi.org/10.3792/pja/1195522169.

7
S. Kailasavalli and C. Yamini, A Study on Anti Fuzzy B-Ideals in Homomorphism and Cartesian product on B-Algebras, International Journal of Computer and Organization Trends, 19, No. 1 (2015), 51-56 , doi: https://doi.org/10.14445/22492593/IJCOT-V19P308.

8
S. M. Mostafa, M. A. Abd-Elnaby and F. Abdel Halim, On KUS-Algebras, International Journal of Algebra, 7, No. 3 (2013), 131-144.

9
S. M. Mostafa, A. T. Hameed, Anti-fuzzy KUS-ideals of KUS-algebras, International Journal of Computer Applications, 70, No. 9 (2013), 24-28.

10
S. M. Mostafa, A. T. Hameed and A. H. Abed, Fuzzy KUS-ideals of KUS-algebras. To appear.

11
S. M. Mostafa, M. A. Abd-Elnaby, and M. M. Yousef, Fuzzy ideals of KU-algebras, International Mathematical Forum, 6, No. 63 (2011), 3139-3149.

12
S. M. Mostafa, M. A. Abd-Elnaby, and M. M. Yousef, Anti-fuzzy KU Ideals of KU-algebras, International Journal of Algebra and Statistics, 1, No. 1 (2012), 92-99, doi: https://doi.org/10.20454/ijas.2012.413.

13
J. Neggers and H. S. Kim, On B-algebras, Matematicki Vesnik, 54, No. 218 (2002), 21-29.

14
T. Priya and T. Ramachandran, Anti Fuzzy Ideals of CI-algebras and its lower level cuts, International Journal of Mathematical Archive, 3, No. 7 (2012), 2524-2529.

15
T. Priya and T. Ramachandran, Some Characterization of Anti-fuzzy PS-ideals of PS-algebras in Homomorphism and Cartesian Products, International Journal of Fuzzy Mathematical Archive, 4, No. 2 (2014), 72-79.

16
T. Senapati, M. Bhowmik and M. Pal, Fuzzy closed ideals of B-algebras, International Journal of Computer Science Engineering and Technology, 1, No. 10 (2011), 669-673.

17
C. Yamini and S. Kailasavalli, Fuzzy B-Ideals on B-Algebras, International Journal of Mathematical Archive, 5, No. 2 (2014), 227-233.

18
L. A. Zadeh, Fuzzy sets, Information and control, 8, No. 3 (1965), 338-353.

How to Cite?

DOI: 10.12732/ijpam.v117i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 3
Pages: 437 - 445


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).