HESITANT FUZZY SETS ON UP-ALGEBRAS

Year 2017, Volume: 5 Issue: 2, 268 - 280, 15.10.2017

P. Mosrıjaı , W. Kamtı , A. Satırad A. Iampan

Abstract

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

Keywords

UP-algebra, hesitant fuzzy set, characteristic hesitant fuzzy set

References

• [1] A. Ali, M. Khan, and 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, and A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc., Manuscript accepted for publication.
• [3] Q. P. Hu and 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 (2017), no. 1, 35{-54.
• [5] Y. Imai and K. Iseki, On axiom system of propositional calculi, XIV, Proc. Japan Acad. 42 (1966), no. 1, 19-22.
• [6] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), no. 1, 26-29.
• [7] Y. B. Jun and S. S. Ahn, Hesitant fuzzy set theory applied to BCI/BCK-algebras, J. Comput. Anal. Appl. 20 (2016), no. 4, 635-646.
• [8] Y. B. Jun, S. S. Ahn, and 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 and S. Z. Song, Hesitant fuzzy set theory applied to lters in MTL-algebras, Honam Math. J. 36 (2014), no. 4, 813-830.
• [10] Y. B. Jun and S. Z. Song, Hesitant fuzzy prelters and lters of EQ-algebras, Appl. Math. Sci. 9 (2015), no. 11, 515-532.
• [11] S. Keawrahun and U. Leerawat, On isomorphisms of SU-algebras, Sci. Magna 7 (2011), no. 2, 39-44.
• [12] C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5 (2009), no. 1, 54-57.
• [13] A. Rezaei and A. B. Saeid, Hesitant fuzzy lters in BE-algebras, Int. J. Comput. Int. Sys. 9 (2016), no. 1, 110-119.
• [14] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12 (2016), no. 6, 739-756.
• [15] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529-539.
• [16] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, 18th IEEE Int. Conf. Fuzzy Syst. (2009), 1378-382.
• [17] L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338-353.
• [18] B. Zhu, Z. Xu, and M. Xia, Dual hesitant fuzzy sets, J. Appl. Math. 2012 (2012), Article ID 879629, 13 pages.