Hesitant Fuzzy Set Theory Applied to Hilbert Algebras
Download PDF
Authors: A. IAMPAN, S. YAMUNADEVI, P. M. MEENAKSHI AND N. RAJESH
DOI: 10.46793/KgJMat2607.1119I
Abstract:
The concept of hesitant fuzzy sets (HFSs) was first introduced by Torra (V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529–539). In this paper, the concept of HFSs to subalgebra, ideals, and deductive systems of Hilbert algebras is introduced. The relationships between hesitant fuzzy subalgebras (HF subalgebras), hesitant fuzzy ideals (HF ideals), and hesitant fuzzy deductive systems (HF deductive systems) and their level subsets are provided.
Keywords:
Hilbert algebra, hesitant fuzzy subalgebra, hesitant fuzzy ideal, hesitant fuzzy deductive system.
References:
[1] B. Ahmad ad A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst. 2009 (2009), Article ID 586507, 6 pages. https://doi.org/10.1155/2009/586507
[2] M. Atef, M. I. Ali and T. Al-Shami, Fuzzy soft covering-based multi-granulation fuzzy rough sets and their applications, Comput. Appl. Math. 40(4) (2021), Article ID 115. https://doi.org/10.1007/s40314-021-01501-x
[3] D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe J. Math. 2 (1985), 29–35.
[4] D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe J. Math. 5 (1988), 161–172.
[5] N. Caǧman, S. Enginoǧlu and F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst. 8(3) (2011), 137–147. https://doi.org/10.22111/ijfs.2011.292
[6] I. Chajda and R. Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J. 39(2) (1999), 429–429.
[7] A. Diego, Sur les algébres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann, Paris) 21 (1966), 1–52.
[8] W. A. Dudek, On fuzzification in Hilbert algebras, Contrib. Gen. Algebra 11 (1999), 77–83.
[9] W. A. Dudek and Y. B. Jun, On fuzzy ideals in Hilbert algebra, Novi Sad J. Math. 29(2) (1999), 193–207.
[10] W. A. Dudek, On ideals in Hilbert algebras, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 38 (1999), 31–34.
[11] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Topics 5(1) (2017), 35–54. https://doi.org/10.22124/jart.2017.2403
[12] A. Iampan, S. Yamunadevi, P. M. Meenakshi and N. Rajesh, Anti-hesitant fuzzy subalgebras, ideals and deductive systems of Hilbert algebras, Math. Stat. 10(5) (2022), 1121–1126. https://doi.org/10.13189/ms.2022.100523
[13] Y. B. Jun, Deductive systems of Hilbert algebras, Math. Japon. 43 (1996), 51–54.
[14] Y. B. Jun and S. S. Ahn, Hesitant fuzzy set theory applied to BCK/BCI-algebras, J. Comput. Anal. Appl. 20(4) (2016), 635–646.
[15] Y. B. Jun, S. S. Ahn and G. Muhiuddin, Hesitant fuzzy soft subalgebras and ideals in BCK/BCI-algebras, Sci. World J. 2014 (2014), Article ID 763929, 7 pages. https://doi.org/10.1155/2014/763929
[16] 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
[17] Y. B. Jun and S.-Z. Song, Hesitant fuzzy prefilters and filters of EQ-algebras, Appl. Math. Sci. 9(11) (2015), 515–532. https://doi.org/10.12988/ams.2015.411962
[18] P. Mosrijai, W. Kamti, A. Satirad and A. Iampan, Hesitant fuzzy sets on UP-algebras, Konuralp J. Math. 5(2) (2017), 268–280. https://doi.org/10.5937/MatMor1802029M
[19] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529–539. https://doi.org/10.1002/int.20418
[20] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, 18th IEEE Int. Conf. Fuzzy Syst. (2009), 1378–1382. https://doi.org/10.1109/FUZZY.2009.5276884
[21] L. A. Zadeh, Fuzzy sets, Inf. Control 8(3) (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
[22] J. Zhan and Z. Tan, Intuitionistic fuzzy deductive systems in Hibert algebra, Southeast Asian Bull. Math. 29(4) (2005), 813–826.
[23] B. Zhu, Z. Xu and M. Xia, Dual hesitant fuzzy sets, J. Appl. Math. 2012 (2012), Article ID 879629, 13 pages. https://doi.org/10.1155/2012/879629
Login:
