Browse > Article
http://dx.doi.org/10.7858/eamj.2015.001

CHARACTERIZATIONS OF HEMIRINGS BY ∊,∊∨q)-FUZZY IDEALS  

Shabir, Muhammad (Department of Mathematics, Quaid-i-Azam University)
Nawaz, Yasir (Department of Mathematics, Quaid-i-Azam University)
Mahmood, Tahir (Department of Mathematics, International Islamic University)
Publication Information
East Asian mathematical journal / v.31, no.1, 2015 , pp. 1-18 More about this Journal
Abstract
In this paper we characterize different classes of hemirings by the properties of their (${\in},{\in}{\vee}q$)-fuzzy ideals, (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and (${\in},{\in}{\vee}q$)-fuzzy bi-ideals.
Keywords
(${\in},{\in}{\vee}q$)-fuzzy ideals; (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals; (${\in},{\in}{\vee}q$)-fuzzy bi-ideals;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Ahsan, Semirings characterized by their fuzzy ideals, J. Fuzzy Math. 6 (1998), 181-192.
2 J. Ahsan, K. Saifullah, M. F. Khan, Fuzzy Semirings, Fuzzy Sets Syst. 60 (1993), 309-320.
3 S. K. Bhakat, $({\in}{\vee}q)$-level subset, Fuzzy Sets and Systems, 103 (1999), 529-533.   DOI   ScienceOn
4 S. K. Bhakat, $({\in},{\in}{\vee}q)$-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and Systems, 112 (2000), 299-312.   DOI   ScienceOn
5 S. K. Bhakat, P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems, 51 (1992), 235-241.   DOI   ScienceOn
6 S. K. Bhakat, P. Das, $({\in},{\in}{\vee}q)$-fuzzy subgroups, Fuzzy Sets and Systems 80 (1996), 359-368.   DOI   ScienceOn
7 S. K. Bhakat, P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81 (1996), 383-393.   DOI   ScienceOn
8 B. Davvaz, $({\in},{\in}{\vee}q)$-fuzzy subnearrings and ideals, Soft Comput, 10 (2006), 206-211.   DOI
9 W. A. Dudek, M. Shabir, M. Irfan Ali, (${\alpha}$, ${\beta}$)-Fuzzy ideals of Hemirings, Comput. Math. Appl., 58 (2009), 310-321.   DOI   ScienceOn
10 W. A. Dudek, M. Shabir, R. Anjum, Characterizations of hemirings by their h-ideals, Comput. Math. Appl., 59 (2010), 3167-3179.   DOI   ScienceOn
11 S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets Syst., 95 (1998), 103-108.   DOI   ScienceOn
12 K. Glazek, A guide to litrature on semirings and their applications in mathematics and information sciences: with complete bibliography, Kluwer Acad. Publ. Nederland, 2002.
13 J. S. Golan, Semirings and their applications, Kluwer Acad. Publ. 1999.
14 U. Hebisch, H. J. Weinert, Semirings: Algebraic Theory and Applications in the Computer Science, World Scientific, 1998.
15 M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6 (1958), 321.
16 K. Iizuka, On Jacobson radical of a semiring, Tohoku Math. J. 11 (1959), 409-421.   DOI
17 X. Ma, J. Zhan, On fuzzy h-ideals of hemirings, J. Syst. Sci. Complexity 20 (2007), 470-478.   DOI
18 Y. B. Jun, M. A. Ozurk, S. Z. Song, On fuzzy h-ideals in hemirings, Inform. Sci. 162 (2004), 211-226.   DOI   ScienceOn
19 Y. B. Jun, S. Z. Song, Generalized fuzzy interior ideals in semigroups, Inform. Sci. 176 (2006), 3079-3093.   DOI   ScienceOn
20 D. R. La Torre, On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12 (1965), 219-226.
21 X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci., 179 (2009), 1249-1268.   DOI   ScienceOn
22 J. N. Mordeson, D. S. Malik, Fuzzy Automata and Languages, Theory and Applications, Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton 2002.
23 V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004), 277-288.   DOI   ScienceOn
24 P. M Pu, Y. M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571-599.   DOI
25 M. Shabir, T. Mahmood, Characterizations of Hemirings by Interval Valued Fuzzy Ideals, Quasigroups and Related Systems, 19 (2011), 317-329.
26 M. Shabir, T. Mahmood, Hemirings characterized by the properties of their fuzzy ideals with thresholds, Quasigroups and Related Systems 18 (2010), 195- 212.
27 H. S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc., 40 (1934), 914-920.   DOI
28 J. Zhan, W. A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci. 177 (2007), 876-886.   DOI   ScienceOn
29 Y. Q. Yin, H. Li, The charatecrizations of h-hemiregular hemirings and h-intrahemiregular hemirings, Inform. Sci. 178 (2008), 3451-3464.   DOI   ScienceOn
30 L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.   DOI