Partial Constant Hesitant Fuzzy Sets on UP-Algebras

In this paper, partial constant hesitant fuzzy sets on UP-algebras are introduced and proved some results. Further, we discuss the relation between partial constant hesitant fuzzy sets and UP-subalgebras (resp. UP-filters, UP-ideals and strongly UP-ideals).

___

  • [1] A. Ali, M. Khan, F. G. Shi, Hesitant fuzzy ideals in Abel-Grassmann's groupoid, Ital. J. Pure Appl. Math. 35 (2015) 537-556.
  • [2] T. Guntasow, S. Sajak, A. Jomkham, A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc. 23(2) (2017) 1-19.
  • [3] Q. P. Hu, X. Li, On BCH-algebras, Math. Semin. Notes, Kobe Univ. 11 (1983) 313-320.
  • [4] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5(1) (2017) 35-54.
  • [5] Y. Imai, K. Is¶eki, On axiom system of propositional calculi, XIV, Proc. Japan Acad. 42(1) (1966) 19-22.
  • [6] K. Is¶eki, An algebra related with a propositional calculus, Proc. Japan Acad. 42(1) (1966) 26-29.
  • [7] Y. B. Jun, S. S. Ahn, Hesitant fuzzy set theory applied to BCI/BCK-algebras, J. Comput. Anal. Appl. 20(4) (2016) 635-646.
  • [8] Y. B. Jun, S. S. Ahn, G. Muhiuddin, Hesitant fuzzy soft subalgebra and ideal in BCI/BCK-algebras, Sci. World J. 2014 (2014) Article ID 763929, 7 pages.
  • [9] Y. B. Jun, K. J. Lee, S. Z. Song, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc. 30(3) (2015) 143-154.
  • [10] Y. B. Jun, S. Z. Song, Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Math. J. 36(4) (2014) 813-830.
  • [11] Y. B. Jun, S. Z. Song, Hesitant fuzzy prefilters and filters of EQ-algebras, Appl. Math. Sci. 9(11) (2015) 515-532.
  • [12] S. Keawrahun, U. Leerawat, On isomorphisms of SU-algebras, Sci. Magna 7(2) (2011) 39-44.
  • [13] P. Mosrijai, W. Kamti, A. Satirad, A. Iampan, Hesitant fuzzy sets on UP-algebras, Konuralp J. Math. 5(2) (2017) 268-280.
  • [14] G. Muhiuddin, Hesitant fuzzy filters and hesitant fuzzy G-filter in residuated lattices, J. Comput. Anal. Appl. 21(2) (2016) 394-404.
  • [15] C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5(1) (2009) 54-57.
  • [16] R. M. Rodriguez, L. Martinez, F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst. 20(1) (2012) 109-119.
  • [17] A. Satirad, P. Mosrijai, W. Kamti, A. Iampan, Level subsets of a hesitant fuzzy set on UP-algebras, Ann. Fuzzy Math. Inform. 14(3) (2017) 279-302.
  • [18] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12(6) (2016) 739-756.
  • [19] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010) 529-539.
  • [20] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, 18th IEEE Int. Conf. Fuzzy Syst. (2009) 1378{1382.
  • 21] L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965) 338-353.
  • [22] B. Zhu, Z. Xu, M. Xia, Dual hesitant fuzzy sets, J. Appl. Math. 2012 (2012) Article ID 879629, 13 pages.