Skip to main content
SpringerLink
Log in

Stratified L-prefilter convergence structures in stratified L-topological spaces

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, a new approach to fuzzy convergence theory in the framework of stratified L-topological spaces is provided. Firstly, the concept of stratified L-prefilter convergence structures is introduced and it is shown that the resulting category is a Cartesian closed topological category. Secondly, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-topological spaces are studied and it is proved that the latter can be embedded in the former as a reflective subcategory. Finally, the relations between the category of stratified L-prefilter convergence spaces and the category of stratified L-Min convergence spaces (fuzzy convergence spaces in the sense of Min) are investigated and it is shown that the former can be embedded in the latter as a reflective subcategory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adámek J, Herrlich H, Strecker GE (1990) Abstract and concrete categories. Wiley, New York

    MATH  Google Scholar 

  • Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24:182–190

    Article  MathSciNet  Google Scholar 

  • Fang JM (2010a) Stratified \(L\)-ordered convergence structures. Fuzzy Sets Syst 161:2130–2149

    Article  MathSciNet  Google Scholar 

  • Fang JM (2010b) Relationships between \(L\)-ordered convergence structures and strong \(L\)-topologies. Fuzzy Sets Syst 161:2923–2944

    Article  MathSciNet  Google Scholar 

  • Güloǧlu M, Coker D (2005) Convergence in \(I\)-fuzzy topological spaces. Fuzzy Sets Syst 151:615–623

    Article  MathSciNet  Google Scholar 

  • Höhle U, Šostak AP (1999) Axiomatic foundations of fixed-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of fuzzy sets: logic, topology, and measure theory, Handbook Series, vol 3. Kluwer, Boston, pp 123–173

    Chapter  Google Scholar 

  • Jäger G (2001) A category of \(L\)-fuzzy convergence spaces. Quaest Math 24:501–517

    Article  MathSciNet  Google Scholar 

  • Jäger G (2005) Subcategories of lattice-valued convergence spaces. Fuzzy Sets Syst 156:1–24

    Article  MathSciNet  Google Scholar 

  • Jäger G (2008) Lattice-valued convergence spaces and regularity. Fuzzy Sets Syst 159:2488–2502

    Article  MathSciNet  Google Scholar 

  • Jäger G (2010a) Compactification of lattice-valued convergence spaces. Fuzzy Sets Syst 161:1002–1010

    Article  MathSciNet  Google Scholar 

  • Jäger G (2010b) Compactness in lattice-valued function spaces. Fuzzy Sets Syst 161:2962–2974

    Article  MathSciNet  Google Scholar 

  • Jäger G (2012a) A one-point compactification for lattice-valued convergence spaces. Fuzzy Sets Syst 190:21–31

    Article  MathSciNet  Google Scholar 

  • Jäger G (2012b) Largest and smallest T\(_2\)-compactifications of lattice-valued convergence spaces. Fuzzy Sets Syst 190:32–46

    Article  Google Scholar 

  • Jäger G (2016) Connectedness and local connectedness for lattice-valued convergence spaces. Fuzzy Sets Syst 300:134–146

    Article  MathSciNet  Google Scholar 

  • Li LQ, Jin Q (2011) On adjunctions between Lim, S\(L\)-Top, and S\(L\)-Lim. Fuzzy Sets Syst 182:66–78

    Article  MathSciNet  Google Scholar 

  • Li LQ, Jin Q (2012) On stratified \(L\)-convergence spaces: pretopological axioms and diagonal axioms. Fuzzy Sets Syst 204:40–52

    Article  MathSciNet  Google Scholar 

  • Li LQ, Jin Q (2014) \(p\)-Topologicalness and \(p\)-regularity for lattice-valued convergence spaces. Fuzzy Sets Syst 238:26–45

    Article  MathSciNet  Google Scholar 

  • Li LQ, Jin Q, Hu K (2015) On stratified \(L\)-convergence spaces: Fischer’s diagonal axiom. Fuzzy Sets Syst 267:31–40

    Article  MathSciNet  Google Scholar 

  • Li LQ, Jin Q, Meng GW, Hu K (2016) The lower and upper \(p\)-topological (\(p\)-regular) modifications for lattice-valued convergence spaces. Fuzzy Sets Syst 282:47–51

    Article  MathSciNet  Google Scholar 

  • Lowen R (1979) Convergence in fuzzy topological spaces. Gen Topl Appl 10:147–160

    Article  MathSciNet  Google Scholar 

  • Lowen E, Lowen R, Wuyts P (1991) The categorical topological approach to fuzzy topology and fuzzy convergence. Fuzzy Sets Syst 40:347–373

    Article  Google Scholar 

  • Lowen E, Lowen R (1992) A topological universe extension of FTS. In: Rodabaugh SE, Klement EP, Höhle U (eds) Applications of category theory to fuzzy sets. Kluwer, Dordrecht

    MATH  Google Scholar 

  • Min KC (1989) Fuzzy limit spaces. Fuzzy Sets Syst 32:343–357

    Article  MathSciNet  Google Scholar 

  • Pang B, Fang JM (2011) \(L\)-fuzzy Q-convergence structures. Fuzzy Sets Syst 182:53–65

    Article  MathSciNet  Google Scholar 

  • Pang B (2013) Further study on \(L\)-fuzzy Q-convergence structures. Iran J Fuzzy Syst 10(5):147–164

    MathSciNet  MATH  Google Scholar 

  • Pang B (2014) On \((L, M)\)-fuzzy convergence spaces. Fuzzy Sets Syst 238:46–70

    Article  Google Scholar 

  • Pang B, Shi F-G (2014) Degrees of compactness of \((L, M)\)-fuzzy convergence spaces and its applications. Fuzzy Sets Syst 251:1–22

    Article  MathSciNet  Google Scholar 

  • Pang B (2014) Enriched \((L, M)\)-fuzzy convergence spaces. J Intell Fuzzy Syst 27:93–103

    MathSciNet  MATH  Google Scholar 

  • Pang B, Zhao Y (2016) Stratified \((L, M)\)-fuzzy Q-convergence spaces. Iran J Fuzzy Syst 14(4):95–111

    MathSciNet  MATH  Google Scholar 

  • Pang B, Zhao Y (2017) Several types of enriched \((L, M)\)-fuzzy convergence spaces. Fuzzy Sets Syst 321:55–72

    Article  MathSciNet  Google Scholar 

  • Pu BM, Liu YM (1980) Fuzzy topology (I), neighborhood structure of a fuzzy point and Moore–Smith convergence. J Math Anal Appl 76:571–599

    Article  MathSciNet  Google Scholar 

  • Preuss G (2002) Foundations of topology: an approach to convenient topology. Kluwer, Dordrecht

    Book  Google Scholar 

  • Wu WC, Fang JM (2012) \(L\)-ordered fuzzifying convergence spaces. Iran J Fuzzy Syst 9(2):147–161

    MathSciNet  MATH  Google Scholar 

  • Xu LS (2001) Characterizations of fuzzifying topologies by some limit structures. Fuzzy Sets Syst 123:169–176

    Article  MathSciNet  Google Scholar 

  • Yao W (2008) On many-valued stratified \(L\)-fuzzy convergence spaces. Fuzzy Sets Syst 159:2503–2519

    Article  MathSciNet  Google Scholar 

  • Yao W (2009) On \(L\)-fuzzifying convergence spaces. Iran J Fuzzy Syst 6(1):63–80

    MathSciNet  MATH  Google Scholar 

  • Yao W (2012) Moore–Smith convergence in \((L, M)\)-fuzzy topology. Fuzzy Sets Syst 190:47–62

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to express their sincere thanks to the anonymous reviewers and the area editor for their careful reading and constructive comments. The first author thanks to the Natural Science Foundation of China (No. 11701122) and the Natural Science Foundation of Guangdong Province (No. 2017A030310584). The second author thanks to the Scientific Research Foundation of CUIT (KYTZ201631, CRF201611, 17ZB0093).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Bin Pang

  2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610000, People’s Republic of China

    Zhen-Yu Xiu

Authors
  1. Bin Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen-Yu Xiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Pang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of this paper.

Additional information

Communicated by A. Di Nola.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pang, B., Xiu, ZY. Stratified L-prefilter convergence structures in stratified L-topological spaces. Soft Comput 22, 7539–7551 (2018). https://doi.org/10.1007/s00500-018-3040-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3040-1

Keywords

Search

Navigation