Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

Young Bae Jun; Seok-Zun Song

Bulletin of the Section of Logic (2020)

  • Volume: 49, Issue: 1
  • ISSN: 0138-0680

Abstract

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Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.

How to cite

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Young Bae Jun, and Seok-Zun Song. "Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras." Bulletin of the Section of Logic 49.1 (2020): null. <http://eudml.org/doc/295587>.

@article{YoungBaeJun2020,
abstract = {Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.},
author = {Young Bae Jun, Seok-Zun Song},
journal = {Bulletin of the Section of Logic},
keywords = {p-semisimple BCI-algebra; Inf-hesitant fuzzy subalgebra; Inf-hesitant fuzzy ideal; Inf-hesitant fuzzy p-ideal},
language = {eng},
number = {1},
pages = {null},
title = {Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras},
url = {http://eudml.org/doc/295587},
volume = {49},
year = {2020},
}

TY - JOUR
AU - Young Bae Jun
AU - Seok-Zun Song
TI - Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 1
SP - null
AB - Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.
LA - eng
KW - p-semisimple BCI-algebra; Inf-hesitant fuzzy subalgebra; Inf-hesitant fuzzy ideal; Inf-hesitant fuzzy p-ideal
UR - http://eudml.org/doc/295587
ER -

References

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  1. [1] A. Al-Masarwah and A. G. Ahmad, m-polar fuzzy ideals of BCK/BCI-algebras, Journal of King Saud University-Science, Vol. 31 (2019), pp. 1220–1226. http://dx.doi.org/10.1016/j.jksus.2018.10.002 
  2. [2] A. Al-Masarwah and A. G. Ahmad, m-Polar (α,β)-fuzzy ideals in BCK/BCIalgebras, Symmetry, Vol. 11 (2019), p. 44. http://dx.doi.org/10.3390/sym11010044 
  3. [3] A. Al-Masarwah and A. G. Ahmad, Novel concepts of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras, International Journal of Innovative Computing, Information and Control, Vol. 14, No. 6 (2018), pp. 2025–2041. 
  4. [4] A. Al-Masarwah and A. G. Ahmad, On some properties of doubt bipolar fuzzy H-ideals in BCK/BCI-algebras, European Journal of Pure and Applied Mathematics, Vol. 11, No. 3 (2018), pp. 652–670. 
  5. [5] Y. Huang, BCI-algebra, Science Press, Beijing, 2006. 
  6. [6] Y. B. Jun and S. S. Ahn, Hesitant fuzzy set theory applied to BCK/BCI-algerbas, Journal of Computational Analysis and Applications, Vol. 20, No. 4 (2016), pp. 635–646. 
  7. [7] Y. B. Jun, G. Muhiuddin, M. A. Ozturk and E. H. Roh, Cubic soft ideals in BCK/BCI algebras, Journal of Computational Analysis and Applications, Vol. 22, No. 5 (2017), pp. 929–940. 
  8. [8] Y. B. Jun and S. Z. Song, Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Mathematical Journal, Vol. 36, No. 4 (2014), pp. 813–830. 
  9. [9] J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co. Seoul, 1994. 
  10. [10] R. M. Rodriguez, L. Martinez and F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems, Vol. 20, No. 1 (2012), pp. 109–119. 
  11. [11] T. Senapati, Y. B. Jun, G. Muhiuddin and K. P. Shum, Cubic intuitionistic structures applied to ideals of BCI-algebras, Analele Universitatii Ovidius Constanta. Seria Matematic, Vol. 27, No. 2 (2019), pp. 213–232. 
  12. [12] V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, Vol. 25 (2010), pp. 529–539. 
  13. [13] 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. 
  14. [14] F. Q. Wang, X. Li and X. H. Chen, Hesitant fuzzy soft set and its applications in multicriteria decision making, Journal of Applied Mathematics, Vol. 2014, Article ID 643785, 10 pages. 
  15. [15] G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems, Vol. 31 (2012), pp. 176–182. 
  16. [16] M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning, Vol. 52, No. 3 (2011), pp. 395–407. 
  17. [17] Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzy sets, Information Sciences, Vol. 181, No. 11 (2011), pp. 2128–2138. 
  18. [18] Z. S. Xu and M. Xia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems, Vol. 26, No. 5 (2011), pp. 410–425. 
  19. [19] X. H. Zhang, H. Jiang and S. A. Bhatti, On p-ideals of a BCI-algebra, Punjab University Journal of Mathematics (Lahore), Vol. 27 (1994), pp. 121–128. 

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