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BIPOLAR FUZZY HYPER MV-DEDUCTIVE SYSTEMS OF HYPER MV-ALGEBRAS

Kang, Min-Su

  • Received : 2010.02.17
  • Published : 2011.04.30

Abstract

The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

Keywords

bipolar fuzzy hyper MV-subalgebra;(weak) bipolar fuzzy hyper MV-deductive system;precisely weak bipolar fuzzy hyper MV-deductive system

References

  1. C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. https://doi.org/10.1090/S0002-9947-1958-0094302-9
  2. D. Dubois and H. Prade, Fuzzy Sets and Systems, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980.
  3. Sh. Ghorbani, On hyper MV-algebras, Ph. D. thesis, Shahbid Bahonar University of Kerman 2007.
  4. Sh. Ghorbani, E. Eslami, and A. Hasankhani, Quotient hyper MV-algebras, Sci. Math. Jpn. 66 (2007), no. 3, 371-386.
  5. Sh. Ghorbani, A. Hasankhani, and E. Eslami, Hyper MV-algebras, Set-Valued Math. Appl. 1 (2008), 205-222.
  6. Y. B. Jun, M. S. Kang, and H. S. Kim, Hyper MV-deductive systems of hyper MV-algebras, Commun. Korean Math. Soc. (submitted). https://doi.org/10.4134/CKMS.2010.25.4.537
  7. Y. B. Jun, S. Y. Kim, and E. H. Roh, Bipolar fuzzy trabslations and extensions of ideals in BCK/BCI-algebras, Tamkang J. Math. (submitted).
  8. 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.
  9. K. J. Lee, Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull. Malays. Math. Sci. Soc. (2) 32 (2009), no. 3, 361-373.
  10. K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand (2000), 307-312.
  11. K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J. Fuzzy Logic Intelligent Systems 14 (2004), 125-129. https://doi.org/10.5391/JKIIS.2004.14.2.125
  12. F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandi-naves, Stockholm (1934), 45-49.
  13. L. Torkzadeh and A. Ahadpanah, Hyper MV -ideals in hyper MV -algebras, MLQ Math. Log. Q. 56 (2010), no. 1, 51-62. https://doi.org/10.1002/malq.200810035
  14. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  15. H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer-Nijhoff Publishing, 1985.