Skip to main content

Hutton L-double uniform spaces

Abstract

We introduce the concept of L-double uniform spaces in Hutton’s sense. We prove the category of L-double uniform spaces is topological category over SET. The natural relationships between L-double uniformities, L-double fuzzy topologies and L-double fuzzy topogenous structures are studied. The family \(\coprod(\eta,\eta^{*})\) of all L-double uniformities \((\mathcal{U},\mathcal{U}^{*})\) compatible with an L-double fuzzy topogenous structure (η, η*) on X is never empty and it contains an L-double uniformity \((\mathcal{U}_{\eta},\mathcal{U}_{\eta^{*}})\), which is the coarsest member of \(\coprod(\eta,\eta^{*}). \)

This is a preview of subscription content, access via your institution.

References

  1. Adamek J, Herrlich H, Strecker GE (1990) Abstract and concrete categories: the joy of cats, Wiley Interscience Pure and Applied Mathematics, Wiley, Brisbane

  2. Atanassov KT, Stoeva S (1983) Intuitionistic fuzzy sets. Polish symposium on interval and fuzzy mathematics, Poznan, pp 23–26

  3. Bayoumi F (2000) The α-levels of a fuzzy uniform structure and of a fuzzy proximity. Fuzzy Sets Syst 116:421–428

    MathSciNet  MATH  Article  Google Scholar 

  4. Bayoumi F (2003) On initial and final uniform structures. Fuzzy Sets Syst 133:299–319

    MathSciNet  MATH  Article  Google Scholar 

  5. Byhan S, Çocker D (2005) Pairwise separation axioms in intuitionistic topological spaces. Hacettepe J Math Stat 34(, 101–114):34S, 101–114

    Google Scholar 

  6. Çoker D (1996) An introduction to fuzzy subspsces in intuitionistic fuzzy topological spaces. J Fuzzy Math 4:749–764

    MathSciNet  MATH  Google Scholar 

  7. Çoker D (1997) An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst 88:81–89

    MATH  Article  Google Scholar 

  8. Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24:39–90

    Article  Google Scholar 

  9. Çoker D, Demirci M (1996) An introduction to intuitionistic fuzzy topological spaces in Šostak’s sense. Busefal 67:67–76

    Google Scholar 

  10. Deschrijver G, Kerre EE (2007) On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Inf Sci 177:1860–1866

    MathSciNet  MATH  Article  Google Scholar 

  11. Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H (2005) Terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets. Fuzzy Sets Syst 156:496–499

    MathSciNet  Article  Google Scholar 

  12. Garcia JG, Rodabaugh SE (2005) Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies. Fuzzy Sets Syst 156:445–484

    MathSciNet  MATH  Article  Google Scholar 

  13. Ghanim MH, Tantawy OA, Selim FM (1996) Gradation of uniformity and gradation of proximity. Fuzzy Sets Syst 79:373–382

    MathSciNet  MATH  Article  Google Scholar 

  14. Höhle U, Rodabaugh SE (1999) Mathematics of fuzzy sets: logic, topology, and measure theory, vol 3, Kluwer, Boston

  15. Hutton BW (1977) Uniformities on fuzzy topological spaces. J Math Anal Appl 53:559–571

    MathSciNet  Article  Google Scholar 

  16. Katsaras AK (1988) Fuzzy quasi-proximities and fuzzy quasi-uniformities. Fuzzy Sets Syst 27:335–343

    MathSciNet  MATH  Article  Google Scholar 

  17. Kim YC (2004) L-fuzzy quasi-uniformizable spaces. Ind J Pure Appl Math 35:599–619

    MATH  Google Scholar 

  18. Kubiak T (1985) On fuzzy topologies, Ph.D. thesis, A. Mickiewicz, poznan

  19. Lee EP, Im YB (2001) Mated fuzzy topological spaces. Int J Fuzzy Logic Intell Syst 11:161–165

    Google Scholar 

  20. Lowen R (1981) Fuzzy uniform spaces. J Math Anal Appl 82:370–385

    MathSciNet  MATH  Article  Google Scholar 

  21. Samanta SK (1995) Fuzzy proximities and fuzzy uniformities. Fuzzy Sets Syst 70:97–105

    MathSciNet  MATH  Article  Google Scholar 

  22. Samanta SK, Mondal TK (1997) Intuitionistic gradation of openness: intuitionistic fuzzy topology. Busefal 73:8–17

    Google Scholar 

  23. Samanta SK, Mondal TK (2002) On intuitionistic gradation of openness. Fuzzy Sets Syst 131:323–336

    MathSciNet  MATH  Article  Google Scholar 

  24. Shi F-G, Zhang J, Zheng C-Y (2003) L-proximities and totally bounded pointwise L-uniformities. Fuzzy Sets Syst 133:321–331

    MathSciNet  MATH  Article  Google Scholar 

  25. Šostak AP (1985) On a fuzzy topological structure. Suppl Rend Circ Matem Palermo-Sir II 11:89–103

    MATH  Google Scholar 

  26. Wang G-J, He Y-Y (2000) Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets Syst 110:271–274

    MathSciNet  MATH  Article  Google Scholar 

  27. Zadeh LA (1965) Fuzzy sets. Inf Cont 8:338–353

    MathSciNet  MATH  Article  Google Scholar 

  28. Zahran AM, Abd-Allah MA, El-Saady K, Ghareeb A (2010) Double fuzzy semi-topogenous structure. J Fuzzy Math 18(2):1–16

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Ghareeb.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ghareeb, A. Hutton L-double uniform spaces. Neural Comput & Applic 21, 181–189 (2012). https://doi.org/10.1007/s00521-011-0758-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-011-0758-4

Keywords

  • L-double fuzzy topology
  • L-double uniform space
  • L-double fuzzy topogenous structure