DOI QR코드

DOI QR Code

IDEAL THEORY IN ORDERED SEMIGROUPS BASED ON HESITANT FUZZY SETS

  • Ahn, Sun Shin (Department of Mathematics Education,Dongguk University) ;
  • Lee, Kyoung Ja (Department of Mathematics Education, Hannam University) ;
  • Jun, Young Bae (Department of Mathematics Education, Gyeongsang National University)
  • Received : 2015.09.25
  • Accepted : 2016.11.10
  • Published : 2016.12.25

Abstract

The notions of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are introduced, and several properties are investigated. Relations between a hesitant fuzzy left (resp., right) ideal,a hesitant fuzzy bi-ideal and a hesitant fuzzy quasi-ideal are discussed. Characterizations of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are considered.

Keywords

References

  1. Y. B. Jun, K. J. Lee and S. Z. Song, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc. 30(3) (2015), 143-154. https://doi.org/10.4134/CKMS.2015.30.3.143
  2. Y. B. Jun and S. Z. Song, Hesitant fuzzy set theory applied to filters in MTL- algebras, Honam Math. J. 36(4) (2014), 813-830. https://doi.org/10.5831/HMJ.2014.36.4.813
  3. Y. B. Jun and S. Z. Song, Hesitant fuzzy prefilters and filters of EQ-algebras, Appl. Math. Sci. 9 (2015), 515-532. https://doi.org/10.12988/ams.2015.411962
  4. Y. B. Jun, S. Z. Song and G. Muhiuddin, Hesitant fuzzy semigroups with a frontier, J. Intell. Fuzzy Systems (in press).
  5. Rosa M. Rodriguez, Luis Martinez and Francisco Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst. 20(1) (2012), 109-119. https://doi.org/10.1109/TFUZZ.2011.2170076
  6. V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529-539.
  7. V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, in: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378-1382.
  8. G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems 31 (2012), 176-182. https://doi.org/10.1016/j.knosys.2012.03.011
  9. M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Internat. J. Approx. Reason. 52(3) (2011), 395-407. https://doi.org/10.1016/j.ijar.2010.09.002
  10. M. Xia, Z. S. Xu and N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making, Group Decision Negotiation 22 (2013), 259-279. https://doi.org/10.1007/s10726-011-9261-7
  11. Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inform. Sci. 181(11) (2011), 2128-2138. https://doi.org/10.1016/j.ins.2011.01.028
  12. B. Zhu, Z. Xu and M. Xia, Hesitant fuzzy geometric Bonferroni means, Inform. Sci. 205 (2012), 72-85. https://doi.org/10.1016/j.ins.2012.01.048