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Interval-Valued Fuzzy Ideals of a Ring

  • Lee, Keon-Chang (Department of Computer Science, Dongshin University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • Received : 2012.05.23
  • Accepted : 2012.09.24
  • Published : 2012.09.25

Abstract

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.

Keywords

References

  1. R.Biswas, "Rosenfeld's fuzzy subgroups with interval-valued membership functions," Fuzzy set and systems, vol. 63, pp. 87-90, 1995.
  2. D.M.Burton, "A First Course in Rings and Ideals"(Addition-Wesley, 1970).
  3. J.Y.Choi, S.R.Kim and K.Hur, "Interval-valued smooth topological spaces," Honam Math.J., vol. 32, pp. 711-738, 2010. https://doi.org/10.5831/HMJ.2010.32.4.711
  4. M.B. Gorzalczany, "A method of inference in approximate reasoning based on interval-valued fuzzy sets," Fuzzy Sets and Systems, vol. 21, pp. 1-17, 1987. https://doi.org/10.1016/0165-0114(87)90148-5
  5. K.Hur, J.G.Lee and J.Y.Choi, "Interval-valued fuzzy relations," J.Korean Institute of Intelligent systems, vol. 19, pp. 425-432, 2009. https://doi.org/10.5391/JKIIS.2009.19.3.425
  6. H.W.Kang, "Interval-valued fuzzy subgroups and homomorphisms," Honam Math. J., vol. 33, 2011.
  7. K.Hur and H.W.Kang, "Interval-valued fuzzy subgroups and rings," Honam Math.J., vol. 32, pp. 593- 617, 2010. https://doi.org/10.5831/HMJ.2010.32.4.593
  8. T.K.Mondal and S.K.Samanta, "Topology of intervalvalued fuzzy sets," Indian J.Pure Appl.Math., vol. 30, pp. 20-38, 1999.
  9. T.K.Mukherjee and M.K.Sen, "On fuzzy ideals of a ring," Fuzzy sets and Systems, vol. 21, pp. 98-104, 1987.
  10. L.A.Zadeh, "Fuzzy sets," Inoform. and Centrol, vol. 8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  11. L.A.Zadeh, "The concept of a linguistic variable and its application to approximate reasoning I," Inform. Sci, vol. 8, pp. 199-249, 1975. https://doi.org/10.1016/0020-0255(75)90036-5