DOI QR코드

DOI QR Code

BIPOLAR FUZZY a-IDEALS OF BCI-ALGEBRAS

Lee, Kyoung-Ja;Jun, Young-Bae

  • Received : 2010.04.21
  • Published : 2011.10.31

Abstract

The notion of bipolar fuzzy a-ideals of BCI-algebras is introduced, and their properties are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals and bipolar fuzzy a-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy a-ideal are provided. Characterizations of bipolar fuzzy a-ideals are given. Using a finite collection of a-ideals, a bipolar fuzzy a-ideal is established.

Keywords

bipolar fuzzy subalgebra;bipolar fuzzy ideal;bipolar fuzzy a-ideal

References

  1. D. Dubois and H. Prade, Fuzzy Sets and Systems, Academic Press, 1980.
  2. Y. B. Jun, H. S. Kim, and K. J. Lee, Bipolar fuzzy translations in BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), no. 3, 399-408.
  3. Y. B. Jun and S. Z. Song, Subalgebras and closed ideals of BCH-algebras based on bipolar-valued fuzzy sets, Sci. Math. Jpn. 68 (2008), no. 2, 287-297.
  4. K. J. Lee, Bipolar fuzzy subalgerbas and bipolar fuzzy ideals of BCK/BCI-algerbas, Bull. Malays. Math. Sci. Soc. 32 (2009), no. 3, 361-373.
  5. K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand (2000), 307-312.
  6. K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Logic Intelligent Systems 14 (2004), no. 2, 125-129. https://doi.org/10.5391/JKIIS.2004.14.2.125
  7. Y. L. Liu and J. Meng, X. H. Zhang, Xiao, and Z. C. Yue, q-ideals and a-ideals in BCI-algebras, Southeast Asian Bull. Math. 24 (2000), no. 2, 243-253. https://doi.org/10.1007/s10012-000-0243-y
  8. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  9. H.-J. Zimmermann, Fuzzy Set Theory and its Applications, Kluwer-Nijhoff Publishing, 1985.

Cited by

  1. m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets vol.2014, 2014, https://doi.org/10.1155/2014/416530