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AIMS Mathematics

2022, Volume 7, Issue 7: 13410-13422. doi: 10.3934/math.2022741
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Research article

Properties of R0-algebra based on hesitant fuzzy MP filters and congruence relations

  • Department of Mathematics, Xi'an Traffic Engineering Institute, 710300, China
  • Received: 25 January 2022 Revised: 25 March 2022 Accepted: 31 March 2022 Published: 18 May 2022

  • MSC : 03G25, 08A72

  • The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of R0-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in R0-algebra.

    Citation: Man Jiang. Properties of R0-algebra based on hesitant fuzzy MP filters and congruence relations[J]. AIMS Mathematics, 2022, 7(7): 13410-13422. doi: 10.3934/math.2022741

    Related Papers:

  • The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of R0-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in R0-algebra.


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    [1] G. J. Wang, Non-classical mathematical logic and approximate reasoning, Beijing: Science Press, 2000.
    [2] G. S. Cheng, G. J. Wang, R0-algebras and its basic structure, J. Math. Phys., S1 (1999), 584-588.
    [3] J. Li, N. J. He, Maximal reduction in R0-algebras, J. Lanzhou Univ. Technol., 41 (2015), 151-154.
    [4] X. J. Hua, Derivation of R0-algebra, Comput. Eng. Appl., 53 (2017), 54-57.
    [5] Z. F. Zhang, H. B. Wu, Generalized relative annihilator in R0-algebras, J. Jilin Univ. 57 (2019), 465-472.
    [6] X. L. Xin, Y. J. Qin, P. F. He, Monadic operators on R0-algebras, Fuzzy Syst. Math., 1 (2016), 48-57.
    [7] F. L. Fan, Y. J. Jie, Boolean atoms in R0-algebra and their applications, J. Shanxi Norm. Univ., 5 (2019), 94-99.
    [8] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
    [9] K. Atanassotv, Intuitionistic fuzzy sets, Fuzzy Set Syst., 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
    [10] W. R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proc. IEEE Conf., 1994,305-309.
    [11] C. H. Liu, Y. M. Li, H. Y. Zhang, Bipolar valued fuzzy ideals negating non involutive residual lattices, J. Shandong Univ., 54 (2019), 88-98.
    [12] H. R. Zhang, Q. G. Li, Intuitionistic fuzzy filter theory on residuated lattices, Soft Comput., 23 (2019), 6777-6783. https://doi.org/10.1007/s00500-018-3647-2 doi: 10.1007/s00500-018-3647-2
    [13] A. X. Zhan, Y. H. Xiao, W. H. Liu, Intuitionistic fuzzy filter theory of BL-algebras, Int. J. Mach. Learn. Cyb., 4 (2013), 659-669. https://doi.org/10.1007/s13042-012-0130-8 doi: 10.1007/s13042-012-0130-8
    [14] J. Revathi, D. Kalamani, K. Arun Prakash, Certain kinds of intuitionistic fuzzy filters of lattice implication algebras, Asian J. Res. Soc. Sci. Humanit., 7 (2017), 234-246. https://doi.org/10.5958/2249-7315.2017.00168.X doi: 10.5958/2249-7315.2017.00168.X
    [15] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 6 (2010), 529-539. https://doi.org/10.1002/int.20418 doi: 10.1002/int.20418
    [16] M. Debabrata, A hesitant intuitionistic fuzzy set approach to study ideals of semirings, Int. J. Fuzzy Syst. Appl., 10 (2021), 1-17. https://doi.org/10.4018/IJFSA.2021070101 doi: 10.4018/IJFSA.2021070101
    [17] Q. Y. Ding, G. Mark, Y. M. Wang, Interval-valued hesitant fuzzy todim method for dynamic emergency responses, Soft Comput., 25 (2021), 11-17. https://doi.org/10.1007/s00500-021-05751-z doi: 10.1007/s00500-021-05751-z
    [18] H. P. Chen, Hesitant fuzzy multi-attribute group decision making method based on weighted power operators in social network and their application, J. Intell. Fuzzy Syst., 40 (2021), 9383-9401. https://doi.org/10.3233/JIFS-201859 doi: 10.3233/JIFS-201859
    [19] H. X. Li, H. B. Wu, Fuzzy sub algebras and fuzzy associative MP filters of R0-algebras, Fuzzy Syst. Math., 22 (2008), 22-26.
    [20] A. Siqveland, Physical interpretation of noncommutative algebraic varieties, J. Phys. Math., 1 (2015), 1-3.
    [21] V. F. Perepelitsa, T. Ekelof, A. Ferrer, B. R. French, Physical interpretation of the anomalous Cherenkov rings observed with the DELPHI detector, High Energy Phys.-Ex., 2020. https://doi.org/10.48550/arXiv.2001.08576 doi: 10.48550/arXiv.2001.08576
    [22] X. L. Ma, J. Zhan, Y. Xu, Generalized fuzzy filters of R0-algebras, Soft Comput., 11 (2007), 1079-1087. https://doi.org/10.1007/s00500-007-0165-z doi: 10.1007/s00500-007-0165-z
    [23] L. Z. Liu, K. T. Li, Fuzzy implicative and Boolean filters of R0-algebras, Inform. Sci., 171 (2005), 61-71. https://doi.org/10.1016/j.ins.2004.04.001 doi: 10.1016/j.ins.2004.03.017
    [24] J. S. Han, Y. B. Jun, H. S. Kim, Fuzzy-fated filters of R0-algebras, Discrete Dyn. Nat. Soc., 2011, 1-9. https://doi.org/10.1155/2011/980315 doi: 10.1155/2011/980315
    [25] J. Zhan, X. L. Ma, Y. B. Jun, (∈, ∈ ∨ q)-fuzzy filters of R0-algebras, Math. Logic Quart., 5 (2009), 493-508.
    [26] Y. B. Jun, K. J. Lee, Redefined fuzzy filters of R0-algebras, Appl. Math. Sci, 5 (2012), 1287-1297.
    [27] J. Zhan, Y. B. Jun, D. W. Pei, Falling fuzzy (implicative) filters of R0-algebras, J. Intell. Fuzzy Syst., 24 (2013), 611-618. https://doi.org/10.3233/IFS-2012-0580 doi: 10.3233/IFS-2012-0580
    [28] G. J. Wang, MV-algebras. BL-algebras, R0-algebras and multiple-valued logic, Appl. Sci., 12 (2022), 1263. doi: 10.3390/app12031263
    [29] Y. B. Jun, J. Zhan, Y. J. Lee, Generalizations of (∈, ∈ ∨ q)-fuzzy filters, Int. J. Math. Math. Sci., 1 (2010).
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