Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 5: 4311-4321. doi: 10.3934/math.2020275
Previous Article Next Article
Research article

$L$-biconvex sets on some fuzzy algebraic substructures

  • 1.
    School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, PR China
  • 2.
    Department of Mathematics, Shantou University, Guangdong, 515063, PR China
  • Received: 26 December 2019 Accepted: 23 April 2020 Published: 08 May 2020

  • MSC : 52A01, 54A40

  • With a complete residuated lattice $L$ as the set of truth values, we first introduce the concept of $L$-biconvex sets. Then we focus on investigating the forms of $L$-biconvex sets on three fuzzy algebraic substructures which are $L$-subsemilattices, $L$-sublattices and $L$-Boolean sublattices.

    Citation: Hui Yang, Yi Shi. $L$-biconvex sets on some fuzzy algebraic substructures[J]. AIMS Mathematics, 2020, 5(5): 4311-4321. doi: 10.3934/math.2020275

    Related Papers:

  • With a complete residuated lattice $L$ as the set of truth values, we first introduce the concept of $L$-biconvex sets. Then we focus on investigating the forms of $L$-biconvex sets on three fuzzy algebraic substructures which are $L$-subsemilattices, $L$-sublattices and $L$-Boolean sublattices.


    加载中


    [1] M. van de Vel, Theory of Convex Structures, North-Holland, Amsterdam, 1993.
    [2] M. V. Rosa, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst., 62 (1994), 97-100. doi: 10.1016/0165-0114(94)90076-0
    [3] Q. Jin, L. Q. Li, On the embedding of L-convex spaces in stratified L-convex spaces, SpringerPlus, 5 (2016), 1610.
    [4] B. Pang, F. G. Shi, Subcategories of the category of L-convex spaces, Fuzzy Sets Syst., 313 (2017), 61-74. doi: 10.1016/j.fss.2016.02.014
    [5] C. Shen, F. G. Shi, Characterizations of L-convex spaces via domain theory, Fuzzy Sets Syst., 380 (2020), 44-63. doi: 10.1016/j.fss.2019.02.009
    [6] B. Pang, F. G. Shi, Fuzzy counterparts of hull spaces and interval spaces in the framework of L-convex spaces, Fuzzy Sets Syst., 369 (2019), 20-39. doi: 10.1016/j.fss.2018.05.012
    [7] B. Pang, Z. Y. Xiu, An axiomatic approach to bases and subbases in L-convex spaces and their applications, Fuzzy Sets Syst., 369 (2019), 40-56. doi: 10.1016/j.fss.2018.08.002
    [8] F. G. Shi, Z. Y. Xiu, A new approach to the fuzzification of convex structures, J. Appl. Anal., 2014 (2014), 1-12.
    [9] F. G. Shi, Z. Y. Xiu, (L, M)-fuzzy convex structures, J. Nonlinear Sci. Appl., 10 (2017), 3655-3669. doi: 10.22436/jnsa.010.07.25
    [10] B. Pang, Hull operators and interval operators in the (L, M)-fuzzy convex spaces, Fuzzy Sets Syst., 2019, DOI: 10.1016/j.fss.2019.11.010.
    [11] B. Pang, Bases and subbases in (L, M)-fuzzy convex spaces, Comput. Appl. Math., 39 (2020), 41.
    [12] C. Y. Liang, F. H. Li, A degree approach to separation axioms in M-fuzzifying convex spaces, J. Intell. Fuzzy Syst., 36 (2019), 2885-2893. doi: 10.3233/JIFS-171361
    [13] C. Y. Liang, F. H. Li, J. Zhang, Separation axioms in (L, M)-fuzzy convex spaces, J. Intell. Fuzzy Syst., 36 (2019), 3649-3660. doi: 10.3233/JIFS-181772
    [14] Z. Y. Xiu, Q. H. Li, B. Pang, Fuzzy convergence structures in the framework of L-convex spaces, Iran. J. Fuzzy Syst., 2020, DOI:10.22111/IJFS.2020.5232.
    [15] D. W. Pei, The characterization of residuated lattices and regular residuated lattices, Acta Mathematica Sinica, 45 (2002), 271-278. (In Chinese)
    [16] Y. Maruyama, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku, 1641 (2009), 22-37.
    [17] N. Ajmal, K. V. Thomas, Fuzzy lattice, Inform. Sci., 79 (1994), 271-291. doi: 10.1016/0020-0255(94)90124-4
    [18] Y. Zhong, F. G. Shi, Formulations of L-convex hulls on some algebraic structures, J. Intell. Fuzzy Syst., 33 (2017), 1-11. doi: 10.3233/JIFS-15982
    [19] J. Jiménez, S. Montes, B. Šešeljia, et al. On lattice valued upsets and down-sets, Fuzzy Sets Syst., 161 (2010), 1699-1710. doi: 10.1016/j.fss.2009.11.012
    [20] Y. Bo, W. W. Ming, Fuzzy ideals on a distributive lattice, Fuzzy Sets Syst., 35 (1990), 231-240. doi: 10.1016/0165-0114(90)90196-D
    [21] G. Birkhoff, Lattice Theory, American Mathematical Society, Providence RI, 1967.
    [22] B. A. Davey, H. A. Priestley, Introduction to Lattice and Order (2 Eds.), Cambridge: Cambridge University Press, 2002.
    [23] M. Bhowmik, T. Senapati, M. Pal, Intuitionistic L-fuzzy ideals of BG-algebras, Afr. Mat., 25 (2014), 577-590. doi: 10.1007/s13370-013-0139-5
    [24] C. Janab, M. Pal, T. Senapatia, et al. Atanassov0s Intuitionistic L-fuzzy G-subalgebras of Galgebras, J. Fuzzy Math., 23 (2015), 325-340.
    [25] J. Meng, Y. B. Jun, BCK-Algebras, Kyung Moon Sa Co., Seoul, Korea, 1994.
    [26] T. Senapatia, C. Janab, M. Bhowmikc, et al. L-fuzzy G-subalgebras of G-algebras, J. Egypt. Math. Soc., 23 (2015), 219-223. doi: 10.1016/j.joems.2014.05.010
  • Reader Comments
  • © 2020 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 3.1

Metrics

Article views(4391) PDF downloads(267) Cited by(1)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog