Fuzzy soft -hemirings
Keywords:
, -hemirings, Fuzzy soft set, -fuzzy soft (left, right) -ideal, -fuzzy soft -interior-ideal, ( -hemiregular, -semisimple) -hemiring.Abstract
Maji et al. (2001) introduced the concept of a fuzzy soft set, which is an extension to the concept of a soft set. The concepts of -fuzzy soft left -ideals (right -ideals, -interior-ideals) in -hemirings are introduced. Some new characterization theorems of these kinds of fuzzy soft -ideals of a -hemiring are also given. Finally, we show that -hemiregular and -semisimple -hemirings can be described by -fuzzy soft -ideals and -fuzzy soft -interior-ideals.References
Aktas, H. Cagman, N. 2007. Soft sets and soft groups. Information Sciences 177 : 2726-2735.
Ali, M. I., Feng, F., Liu, X., Min, W. K. Shabir, M. 2009. On some new operations in soft set theory. Computers and Mathematics with Applications 57 : 1547-1553.
Barnes, W. E. 1996. On the rings of Nobusawa. Pacific Journal of Mathematics 18 : 411-422.
Cagman, N. Enginoglu, S. 2010. Soft matrix theory and its decision making. Computers and Mathematics with Applications 59 : 3308-3314.
Dudek, W. A., Shabir, M. Ali, M. I. 2009. (α ,β)-fuzzy ideals of hemirings. Computers and Mathematics with Applications 58 : 310-321.
Dudek, W. A., Shabir, M. Anjum, R. 2010. Characterizations of hemirings by their >h>-ideals. Computers and Mathematics with Applications 59 : 3167-3179.
Dutta, T. K. Chanda, T. 2005. Structures of fuzzy ideals of rings. Bulletin of Malaysian Mathematical Sciences Society 28 : 9-15.
Dutta, T. K Sardar, S. K. 2002. On the operator semirings of a -semirings. Southeast Bulletin of Mathematics 26 : 203-213.
Feng, F., Jun, Y. B., Liu, X. Li, L. 2010. An adjusta ble approach to fuzzy soft set based decision making. Journal of Computation Applied Mathematics 234 : 10-20.
Feng, F., Jun, Y. B. Zhao, X. 2008. Soft semirings. Computers and Mathematics with Applications 56 : 2621-2628.
Inan, E. Ozturk, M. A. 2012. Fuzzy soft rings and fuzzy soft ideals. Neural Computation and Applications 21 :s1-s8.
Jun, Y. B. 1995. On fuzzy prime ideals of -rings. Soochow Journal Mathematics 21 : 41-48.
Jun, Y. B. 2008. Soft BCK/BCI-algebras. Computers and Mathematics with Applications 56 : 1408-1413.
Jun, Y. B. Lee, C.Y. 1992. Fuzzy -rings. Pusan Kyongnan Math. J. (presently, East Asian Mathematics Journal) 8 : 163-170.
Jun, Y. B., Ozturk, M. A. Song, S. Z. 2004. On fuzzy h-ideals in hemirings. Information Sciences 162 : 211-226.
Kyuno, S., Nobusawa, N. Sith, N. B. 1987. Regular gamma rings. Tsukuba Journal Mathematics 11 : 371-382.
Ma, X., Yin, Y. Zhan, J. 2012. Characterizations of h-intra- and h -quasi-hemiregular hemirings. Computers and Mathematics with Applications 63 : 783-793.
Ma, X. Zhan, J. 2007. On fuzzy h-ideals of hemirings. Journal of Systems and Sciences Complexity 20 : 470-478.
Ma, X. Zhan, J. 2009. Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings. Information Sciences 179 : 1249-1268.
Ma, X. Zhan, J. 2010. Fuzzy h-ideals in h-hemiregular and h-semisimple -hemirings. Neural Computation and Application 19 : 477-485.
Ma, X., Zhan, J. Shum, K. P. 2011. Generalized fuzzy h-ideals of hemirings. Bulletin of Malaysian Mathematical Sciences Society 34 : 561-574.
Maji, P. K., Biswas, R. Roy, A. R. 2001. Fuzzy soft sets. Journal of Fuzzy Mathematics 9 : 589-602.
Maji, P. K., Biswas, R. Roy, A. R. 2003. Soft set theory. Computers and Mathematics with Applications 45 : 555-562.
Maji, P. K., Roy, A. R. Biswas, R. 2002. An application of soft sets in a decision making problem. Computers and Mathematics with Applications 44 : 1077-1083.
Majumdar, P. Samanta, S. K. 2010. Generalised fuzzy soft sets. Computers and Mathematics with Applications 59 : 1425-1432.
Molodtsov, D. 1999. Soft set theory-first results. Computers and Mathematics with Applications 37 : 19-31.
Ozturk, M. A., Uckum, M. Jun, Y. B. 2002. Characterizations of Artinian and Noetherian gamma-rings in terms of fuzzy ideals. Turkish Journal of Mathematics 27 : 199-205.
Ozturk, M. A., Uckum, M. Jun, Y. B. 2003. Fuzzy ideals in Gamma-rings. Turkish Journal of Mathematics 27 : 369-374.
Qin, K. Y. Hong, Z. 2010. On soft equality. Journal of Computation Applied Mathematics 234 : 1347-1355.
Rao, M. K. 1995. -semirings-1. Southeast Bulletin of Mathematics 19 : 49-54.
Sardar, S. K. Mandal, D. 2009. Fuzzy h-ideal in -hemiring. International Journal of Pure and Applied Mathematics 56 : 439-450.
Sezgin, A. Atagun, A. O. 2011. Soft groups and normalistic soft groups. Computers and Mathematics with Applications 62 : 685-698.
Yang, C. F. 2011. Fuzzy soft semigroups and fuzzy soft ideals. Computers and Mathematics with Applications 61 : 255-261.
Yin, Y., Huang, X., Xu, D. Li, H. 2009. The characterizations of h-semisimple hemirings. International Journal of Fuzzy Systems 11 : 116-122.
Yin, Y., Jun, Y. B. Zhan, J. 2011. Vague soft hemirings. Computers and Mathematics with Applications 62 : 199-213.
Yin, Y. Li, H. 2008. The characterizations of h-hemiregular hemirings and h-intra- hemiregular hemirings. Information Sciences 178 : 3451-3464.
Yin, Y. Zhan, J. 2012. The characterizations of hemirings in terms of fuzzy soft h-ideals, Neural Computation and Applications 21 : S43-S57.
Zadeh, place City L. A. 1965. Fuzzy sets. Information and Control 8 : 338-353.
Zhan, J. Davvaz, B. 2007. L-fuzzy h-ideals with operators in hemirings. Northeast Mathematics Journal 23 : 1-14, in Chinese.
Zhan, J. Dudek, W. A. 2007. Fuzzy h-ideals of hemirings. Information Sciences 177 : 876-886.
Zhan, J. Jun, Y. B. 2010. Soft BL-algebras based on fuzzy sets. Computers and Mathematics with Applications 59 : 2037-2046.
Zhan, J. Shum, K. P. 2011. On fuzzy h-ideals in -hemirings. Neural Computation and Applications 20 : 495-505.
