참고문헌
- J. Ahsan, Semirings characterized by their fuzzy ideals, J. Fuzzy Math. 6 (1998), 181-192.
- J. Ahsan, K. Saifullah, M. F. Khan, Fuzzy Semirings, Fuzzy Sets Syst. 60 (1993), 309-320.
-
S. K. Bhakat,
$({\in}{\vee}q)$ -level subset, Fuzzy Sets and Systems, 103 (1999), 529-533. https://doi.org/10.1016/S0165-0114(97)00158-9 -
S. K. Bhakat,
$({\in},{\in}{\vee}q)$ -fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and Systems, 112 (2000), 299-312. https://doi.org/10.1016/S0165-0114(98)00029-3 - S. K. Bhakat, P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems, 51 (1992), 235-241. https://doi.org/10.1016/0165-0114(92)90196-B
-
S. K. Bhakat, P. Das,
$({\in},{\in}{\vee}q)$ -fuzzy subgroups, Fuzzy Sets and Systems 80 (1996), 359-368. https://doi.org/10.1016/0165-0114(95)00157-3 - S. K. Bhakat, P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81 (1996), 383-393. https://doi.org/10.1016/0165-0114(95)00202-2
-
B. Davvaz,
$({\in},{\in}{\vee}q)$ -fuzzy subnearrings and ideals, Soft Comput, 10 (2006), 206-211. https://doi.org/10.1007/s00500-005-0472-1 -
W. A. Dudek, M. Shabir, M. Irfan Ali, (
${\alpha}$ ,${\beta}$ )-Fuzzy ideals of Hemirings, Comput. Math. Appl., 58 (2009), 310-321. https://doi.org/10.1016/j.camwa.2009.03.097 - W. A. Dudek, M. Shabir, R. Anjum, Characterizations of hemirings by their h-ideals, Comput. Math. Appl., 59 (2010), 3167-3179. https://doi.org/10.1016/j.camwa.2010.03.003
- S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets Syst., 95 (1998), 103-108. https://doi.org/10.1016/S0165-0114(96)00306-5
- K. Glazek, A guide to litrature on semirings and their applications in mathematics and information sciences: with complete bibliography, Kluwer Acad. Publ. Nederland, 2002.
- J. S. Golan, Semirings and their applications, Kluwer Acad. Publ. 1999.
- U. Hebisch, H. J. Weinert, Semirings: Algebraic Theory and Applications in the Computer Science, World Scientific, 1998.
- M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6 (1958), 321.
- K. Iizuka, On Jacobson radical of a semiring, Tohoku Math. J. 11 (1959), 409-421. https://doi.org/10.2748/tmj/1178244538
- Y. B. Jun, M. A. Ozurk, S. Z. Song, On fuzzy h-ideals in hemirings, Inform. Sci. 162 (2004), 211-226. https://doi.org/10.1016/j.ins.2003.09.007
- Y. B. Jun, S. Z. Song, Generalized fuzzy interior ideals in semigroups, Inform. Sci. 176 (2006), 3079-3093. https://doi.org/10.1016/j.ins.2005.09.002
- D. R. La Torre, On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12 (1965), 219-226.
- X. Ma, J. Zhan, On fuzzy h-ideals of hemirings, J. Syst. Sci. Complexity 20 (2007), 470-478. https://doi.org/10.1007/s11424-007-9043-0
- X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci., 179 (2009), 1249-1268. https://doi.org/10.1016/j.ins.2008.12.014
- J. N. Mordeson, D. S. Malik, Fuzzy Automata and Languages, Theory and Applications, Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton 2002.
- V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004), 277-288. https://doi.org/10.1016/j.ins.2003.07.008
- 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. https://doi.org/10.1016/0022-247X(80)90048-7
- M. Shabir, T. Mahmood, Characterizations of Hemirings by Interval Valued Fuzzy Ideals, Quasigroups and Related Systems, 19 (2011), 317-329.
- M. Shabir, T. Mahmood, Hemirings characterized by the properties of their fuzzy ideals with thresholds, Quasigroups and Related Systems 18 (2010), 195- 212.
- 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. https://doi.org/10.1090/S0002-9904-1934-06003-8
- Y. Q. Yin, H. Li, The charatecrizations of h-hemiregular hemirings and h-intrahemiregular hemirings, Inform. Sci. 178 (2008), 3451-3464. https://doi.org/10.1016/j.ins.2008.04.002
- L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
- J. Zhan, W. A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci. 177 (2007), 876-886. https://doi.org/10.1016/j.ins.2006.04.005