On Bipolar Valued Fuzzy ð’Œ-Ideals in Hemirings
Abstract
In this paper we discuss some results associated with Bipolar valued fuzzy 𑘠-ideals of hemirings. We also define bipolar valued fuzzy ð‘˜-intrinsic product and characterize ð‘˜- hemiregularhemirings by using their bipolar valued fuzzy𑘠-ideals.References
H.S. Vandiver, “Note on a simple type of algebra in which
cancellation law of addition does not holdâ€, Bull. Amer. Math.
Soc., vol. 40, pp. 914-920, 1934.
J.S. Golan, “Semirings and their applicationsâ€, Kluwer Acad. Publ,
U. Hebisch and H. J. Weinert, “Semirings: Algebraic Theory and
Appl. in the Comp. Sci.â€, World Scientific, 1998.
M. Henriksen, “Ideals in semirings with commutative additionâ€,
Amer. Math. Soc. Notices, 1958.
L.A. Zadeh, “Fuzzy setsâ€, Information and Control, vol. 8, pp.
-353, 1965.
A. Rosenfeld, “Fuzzy groupsâ€, J. Math. Anal. Appl., vol. 35, pp.
-517, 1971.
J. Ahsan, K. Saifullah and M. F. Khan, “Fuzzy semiringsâ€, Fuzzy
Sets and Systems, vol. 60, pp. 309-320, 1993.
[8] J. Ahsan, “Semirings characterized by their fuzzy idealsâ€,
J. Fuzzy Math., vol. 6, pp. 181-192, 1998.
W. Wechler, “The concept of fuzziness in automata and language
theoryâ€, Akademicverlog, Berlin, 1978.
H. J. Zimmermann, “Fuzzy Set Theory and its Applicationsâ€,
Kluwer Nijhoff Publishing, 1985.
K. M. Lee, “Bipolar-valued fuzzy sets and their operationsâ€, Proc.
Int. Conf. on Intelligent Technologies, Bangkok, Thailand,
proc., vol. 307312, 2000.
Y. B. Jun and S.Z. Song, “Subalgebras and Closed Ideals of BCHAlgebras Based on Bipolar-Valued Fuzzy Setsâ€, Sci. Math. Jpn.,
vol. 37, pp. 427-437, 2008.
Y. B. Jun and C. H. Park, “Filters of BCH-algebras based on
bipolar-valued fuzzy setsâ€, Int. Mathematical Forum, vol. 4, pp.
-643, 2009.
K. J. Lee, “Bipolar Fuzzy subalgebras and bipolar fuzzy ideals of
BCK/BCI-algebrasâ€, Bulletin of Malaysian Mathematical Sciences
Society, vol. 32, pp. 361-373, 2009.
T. Mahmood and M. Munir, “On bipolar fuzzy subgroupsâ€, World
Applied Sciences Journal, vol. 27, pp. 1806-1811, 2013.
M. Shabir, and R. Anjum, “Characterization of hemirings by their
k-idealsâ€, Applied Mathematics, vol. 4, pp. 753-768, 2013.
M. K. Sen and P. Mukhopadhyay, "Von NewumannRegularity in
Semirings, "Kyungpook Mathematical Journal, vol. 35, pp. 249-
, 1995.