Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Bipolar fuzzy ideals of Near Rings

  • Received : 2012.02.22
  • Accepted : 2012.06.11
  • Published : 2012.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

Based on the theory of a bipolar fuzzy set, the notion of a bipolar fuzzy subring/ideal of a Near ring is introduced and related properties are investigated. Characterizations of a bipolar fuzzy subnear ring and a bipolar fuzzy ideal in near ring are established. Relations between a bipolar fuzzy ideal and a level cut are discussed. Using bipolar fuzzy ideals, we discuss characterizations of Noetherian Near ring.

Keywords

Acknowledgement

Supported by : 울산과학대학교

References

  1. Interval-Valued H-Fuzzy Sets, Lee, Keon-Chang;Lee, Jeong-Gon; Hur, Kul / International Journal of Fuzzy Logic and Intelligent Systems, v.10, no.2, pp.134-141, 2010. https://doi.org/10.5391/IJFIS.2010.10.2.134
  2. S. Abou-Zaid, On fuzzy subnear-rings and ideals, Fuzzy Sets and Sys., Vol. 44,No.1,pp.139-146,1991. https://doi.org/10.1016/0165-0114(91)90039-S
  3. M.Akram Bipolar fuzzy graphs Information Sciences, Vol. 181, No.24, pp. 5548-5564, 2011. https://doi.org/10.1016/j.ins.2011.07.037
  4. Y. B. Jun and S. Z. Song, Subalgebras and closed ideals of BCH-algebras based on bipolar-valued fuzzy sets, Sci. Math. Jpn., Vol.68, No.2, pp.287-297, 2008.
  5. K.C. Lee,J.G Lee, K.Hur, Interval-Valued H-Fuzzy Sets, International Journal of Fuzzy Logic and Intelligent Systems, Vol.10, No.2, pp.134-141, 2010. https://doi.org/10.5391/IJFIS.2010.10.2.134
  6. K. J. Lee, Bipolar fuzzy subalgerbas and bipolar fuzzy ideals of BCK/BCI-algerbas,Bull. Malays. Math. Sci. Soc., Vol.32, No.3, pp.361-373,2009.
  7. Y. B. Jun and C. H. Park, Filters of BCH-Algebras based on bi-polar-valued fuzzy sets, Int. Math. Forum, Vol.14.,No.13,pp.631-643, 2009.
  8. Y. B. Jun and J. Kavikumar, Bipolar fuzzy finite state machines,Bull. Malays. Math. Sci.Soc. Vol,34,No.1, pp.181-188,2011.
  9. K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, pp.307-312, 2000.
  10. K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Logic Intelligent Systems, Vol.14,No.2, pp.125-129, 2004.
  11. J.H.Park, Y.C.Kwun, M.J.Son, A Generalized Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems International Journal of Fuzzy Logic and Intelligent Systems, Vol.11, No.2, pp.71- 76, 2011. https://doi.org/10.5391/IJFIS.2011.11.2.071
  12. J.H.park,Operations on Generalized Intuitionistic Fuzzy Soft Sets International Journal of Fuzzy Logic and Intelligent Systems, Vol.11, No.3, pp.184-189, 2011. https://doi.org/10.5391/IJFIS.2011.11.3.184
  13. G.Pilz, Near-Rings, North-Holland Publishing Company, Amsterdam ,New York-Oxford,1983.
  14. L. A. Zadeh,Fuzzy sets, Inform. and Control, Vol.8. No.3, pp.338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X