\((\inf, \sup)\)-Hesitant Fuzzy Subalgebras of BCK/BCI-Algebras

Volume 29, Issue 2, pp 142--155 http://dx.doi.org/10.22436/jmcs.029.02.04

Publication Date: August 24, 2022 Submission Date: May 27, 2022 Revision Date: June 14, 2022 Accteptance Date: July 07, 2022

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 688 Downloads
• 1995 Views

Authors

N. Chunsee - Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand. R. Prasertpong - Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand. P. Khamrot - Department of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna of Phitsanulok, Phitsanulok 65000, Thailand. T. Gaketem - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao, Phayao 56000, Thailand. A. Iampan - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao, , Phayao 56000, Thailand. P. Julatha - Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

Abstract

In this paper, we introduce the concept of \((\inf, \sup)\)-hesitant fuzzy subalgebras, which is a general concept of interval-valued fuzzy subalgebras, in BCK/BCI-algebras and investigate its properties. We characterize \((\inf, \sup)\)-hesitant fuzzy subalgebras in terms of sets, fuzzy sets, hesitant fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, negative fuzzy sets and bipolar fuzzy sets. Furthermore, characterizations of subalgebras, fuzzy subalgebras, anti-fuzzy subalgebras, negative fuzzy subalgebras, Pythagorean fuzzy subalgebras and bipolar fuzzy subalgebras of BCK/BCI-algebras are given in terms of \((\inf, \sup)\)-hesitant fuzzy subalgebras and interval-valued fuzzy subalgebras.

Share and Cite

Keywords

• BCK/BCI-algebra
• hesitant fuzzy subalgebra
• \((\inf, \sup)\)-hesitant fuzzy subalgebra
• interval-valued fuzzy subalgebra
• Pythagorean fuzzy subalgebra
• bipolar fuzzy subalgebra

MSC

•  03B52
•  03G25
•  06F35
•  08A72

References

• [1] M. A. Ansari, Rough set theory applied to JU-algebras, Int. J. Math. Comput. Sci., 16 (2021), 1371--1384
  • View Article


• [2] M. A. Ansari, A. Haider, A. N. A. Koam, On JU-algebras and p-closure ideals, Int. J. Math. Comput. Sci., 15 (2020), 135--154
  • View Article


• [3] M. A. Ansari, A. Iampan, Generalized rough $(m, n)$ bi-$\Gamma$-ideals in ordered LA-$\Gamma$-semigroups, Commun. Math. Appl., 12 (2021), 545--557
  • View Article


• [4] R. K. Bandaru, On BRK-algebras,, Int. J. Math. Math. Sci., 2012 (2012), 12 pages
  • View Article


• [5] R. K. Bandaru, N. Rafi, On G-algebras,, Sci. Magna, 8 (2012), 1--7
  • View Article


• [6] R. K. Bandaru, A. B. Saeid, Y. B. Jun, On GE-algebras, Bull. Sect. Logic Univ. Łódź., 50 (2021), 81--96
  • View Article


• [7] H. Harizavi, Y. B. Jun, $\mathrm{SUP}$-hesitant fuzzy quasi-associative ideals of BCI-algebras, Filomat, 34 (2020), 4189--4197
  • View Article


• [8] S. M. Hong, Y. B. Jun, Anti-fuzzy ideals in BCK-algebras, Kyungpook Math. J., 38 (1998), 145--150
  • View Article


• [9] Y. Huang, BCI-algebra, Science Press, Beijing (2006)
  • View Article


• [10] A. Iampan, P. Julatha, P. Khamrot, D. A. Romano, Independent UP-algebras, J. Math. Comput. Sci., 27 (2022), 65--76
  • View Article


• [11] Y. Imai, K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42 (1966), 19--22
  • View Article


• [12] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26--29
  • View Article


• [13] K. Iseki, S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon., 23 (1978/79), 1--26
  • View Article


• [14] U. Jittburus, P. Julatha, New generalizations of hesitant and interval-valued fuzzy ideals of semigroups, Adv. Math. Sci. J., 10 (2021), 2199--2212
  • View Article


• [15] U. Jittburus, P. Julatha, $\inf$-hesitant fuzzy interior ideals of semigroups, Int. J. Math. Comput. Sci., 17 (2022), 775--783
  • View Article


• [16] U. Jittburus, P. Julatha, A. Iampan, INF-Hesitant fuzzy ideals of semigroups and their INF-hesitant fuzzy translations, J. Discrete Math. Sci. Cryptogr., 2022 (2022), (accepted)


• [17] P. Julatha, A. Iampan, A new generalization of hesitant and interval-valued fuzzy ideals of ternary semigroups, Int. J. Fuzzy Log. Intell. Syst., 21 (2021), 169--175
  • View Article


• [18] P. Julatha, A. Iampan, $\inf$-Hesitant and $(sup, inf)$-hesitant fuzzy ideals of ternary semigroups, Missouri J. Math. Sci., 2022 (2022), (accepted)


• [19] P. Julatha, A. Iampan, On $\inf$-Hesitant Fuzzy $\Gamma$-Ideals of $\Gamma$-Semigroups, Adv. Fuzzy Syst., 2022 (2022), 8 pages
  • View Article


• [20] P. Julatha, A. Iampan, $\SUP$-Hesitant fuzzy ideals of $\Gamma$-semigroups, J. Math. Comput. Sci., 26 (2022), 148--161
  • View Article


• [21] Y. B. Jun, Interval-valued fuzzy subalgebras/ideals in BCK-algebras, Sci. Math., 3 (2000), 435--444
  • View Article


• [22] Y. B. Jun, Subalgebras and ideals of BCK/BCI-algebras in framework of the hesitant intersection, Kyungpook Math. J., 56 (2016), 371--386
  • View Article


• [23] Y. B. Jun, S. S. Ahn, Hesitant fuzzy set theory applied to BCK/BCI-algebras, J. Comput. Anal. Appl., 20 (2016), 635--646
  • View Article


• [24] Y. B. Jun, M. S. Kang, C. H. Park, N-Subalgebras in BCK/BCI-algebras based on point N-structures, Int. J. Math. Math. Sci., 2010 (2010), 9 pages
  • View Article


• [25] Y. B. Jun, K. J. Lee, S. Z. Song, N-Ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc., 22 (2009), 417--437
  • View Article


• [26] Y. B. Jun, S.-Z. Song, INF-hesitant fuzzy ideals in BCK/BCI-algebras, Bull. Sect. Logic Univ. Łódź., 49 (2020), 53--78
  • View Article


• [27] H. S. Kim, Y. H. Kim, On BE-algebras, Sci. Math. Japon., 66 (2007), 113--116
  • View Article


• [28] K. J. Lee, Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull. Malays. Math. Sci. Soc. (2), 32 (2009), 361--373
  • View Article


• [29] J. Meng, Y. B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul (1994)
  • Google Scholar


• [30] M. Mohseni Takallo, R. A. Borzooei, Y. B. Jun, Sup-Hesitant Fuzzy p-Ideals of BCI-Algebras, Fuzzy Inf. Eng., 13 (2021), 460--469
  • View Article


• [31] P. Mosrijai, A. Satirad, A. Iampan, New types of hesitant fuzzy sets on UP-algebras, Math. Morav., 22 (2018), 29--39
  • View Article


• [32] G. Muhiuddin, Hesitant fuzzy filters and hesitant fuzzy G-filters in residuated lattices, J. Comput. Anal. Appl., 21 (2016), 394--404
  • View Article


• [33] G. Muhiuddin, A. M. Alanazi, M. E. Elnair, K. P. Shum, Inf-hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras, Eur. J. Pure Appl. Math., 13 (2020), 9--18
  • View Article


• [34] G. Muhiuddin, H. Harizavi, Y. B. Jun, Ideal theory in BCK/BCI-algebras in the frame of hesitant fuzzy set theory, Appl. Appl. Math., 15 (2020), 337--352
  • View Article


• [35] G. Muhiuddin, Y. B. Jun, Sup-hesitant fuzzy subalgebras and its translations and extensions, Ann. Commun. Math., 2 (2019), 48--56
  • View Article


• [36] G. Muhiuddin, H. S. Kim, S. Z. Song, Y. B. Jun, Hesitant fuzzy translations and extensions of subalgebras and ideals in BCK/BCI-algebras, J. Intell. Fuzzy Syst., 32 (2017), 43--48
  • View Article


• [37] G. Muhiuddin, A. Mahboob, M. Balamurugan, Hesitant anti-intuitionistic fuzzy soft commutative ideals of BCKalgebras, Ann. Commun. Math., 3 (2020), 158--170
  • View Article


• [38] P. Phummee, S. Papan, C. Noyoampaeng, U. Jittburus, P. Julatha, A. Iampan, $\sup$-hesitant fuzzy interior ideals of semigroups and their $\sup$-hesitant fuzzy translations, Int. J. Innov. Comput. Inf. Control, 18 (2022), 121--132
  • View Article


• [39] C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna, 5 (2009), 54--57
  • View Article


• [40] V. S. Subha, P. Dhanalakshmi, New type of fuzzy ideals in BCK/BCI-algebras, World Sci. News, 153 (2021), 80--92
  • View Article


• [41] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529--539
  • View Article


• [42] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, In: IEEE International Conference on Fuzzy Systems (Jeju, Korea South), 2009 (2009), 1378--1382
  • View Article


• [43] O. G. Xi, Fuzzy BCK-algebras, Math. Japon., 36 (1991), 935--942
  • MathSciNet


• [44] R. R. Yager, Pythagorean fuzzy subsets, Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (Edmonton, Canada), 2013 (2013), 57--61
  • View Article


• [45] R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., 28 (2013), 436--452
  • View Article


• [46] L. A. Zadeh, Fuzzy sets,, Inf. Control, 8 (1965), 338--353
  • View Article


• [47] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning–I, Information Sci., 8 (1975), 199--249
  • View Article


• [48] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, 1994 (1994), 305--309
  • View Article