Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 7: 13410-13422. doi: 10.3934/math.2022741
Previous Article Next Article
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.


    加载中


    [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).
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1778) PDF downloads(51) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(3)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog