Acta Mathematica Sinica, English Series

, Volume 28, Issue 9, pp 1787–1798 | Cite as

On fuzzy preordered structures and (Fuzzy) hyperstructures

  • Irina Cristea
  • Morteza Jafarpour
  • Seyed Sh. Mousavi
Article
First Online:
Received:
Revised:
Accepted:

Abstract

This article presents a connection between fuzzy preordered structures and hyperstructures. Firstly, we introduce the notion of fuzzy preordered semigroup and then, we construct a semihypergroup associated with it, giving some properties of the associated hyperstructure. Secondly, we define the notion of fuzzy preordered ring in order to construct a fuzzy hyperring.

Keywords

Fuzzy preordered semigroup hypergroup fuzzy hyperring mutually associativity 

MR(2000) Subject Classification

20N20 03E72 06F05 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

10114_2012_314_MOESM1_ESM.tex (42 kb)
Supplementary material, approximately 42.1 KB.

References

  1. [1]
    Borzooei, R. A., Bakhshi, M.: Lattice structure on fuzzy congruence relations of hypergroupoid. Inform. Sci., 177, 3305–3313 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Corsini, P.: Fuzzy sets, join spaces and factor spaces. Pure Math. Appl., 20, 439–446 (2000)MathSciNetGoogle Scholar
  3. [3]
    Corsini, P., Leoreanu-Fotea, V.: Join spaces associated with fuzzy sets. J. Combinatorics Inf. Syst. Sci., 20(1–4), 293–303 (1995)MathSciNetMATHGoogle Scholar
  4. [4]
    Corsini, P., Leoreanu-Fotea, V.: Fuzzy sets and join spaces associated with rough sets. Rend. Circ. Math. Palermo, 51, 527–536 (2002)MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Corsini, P., Leoreanu-Fotea, V.: Applications of Hyperstructure Theory, Kluwer Academic Publisher, Dordrecht, 2003MATHGoogle Scholar
  6. [6]
    Cristea, I., Davvaz, B.: Atanassov’s intuitionistic fuzzy grade of hypergroups. Inform. Sci., 180, 1506–1517 (2010)MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Cristea, I., Hoskova, S.: Fuzzy pseudotopological hypergroupoids. Iran. J. Fuzzy Syst., 6(4), 11–19 (2009)MathSciNetMATHGoogle Scholar
  8. [8]
    Davvaz, B., Zhan, J., Shum, K. P.: Generalized fuzzy H v-submodules endowed with interval valued membership functions. Inform. Sci., 178, 3147–3159 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Stefanescu, M., Cristea, I.: On the fuzzy grade of hypergroups. Fuzzy Sets and Systems, 159, 1097–1106 (2008)MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Vougiouklis, J.: ∂-operations and H v-fields. Acta Mathematica Sinica, English Series, 24, 1067–1078 (2008)MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Zahedi, M. M., Ameri, R.: On the prime, primary and maximal subhypermodules. Ital. J. Pure Appl. Math., 18, 61–80 (1999)MathSciNetGoogle Scholar
  12. [12]
    Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl., 35, 512–517 (1971)MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    Davvaz, B.: Fuzzy H v-groups. Fuzzy Sets and Systems, 101, 191–195 (1999)MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Sen, M. K., Ameri, R., Chowdhury, G.: Fuzzy hypersemigroups. Soft Comput., 12(9), 891–900 (2008)CrossRefMATHGoogle Scholar
  15. [15]
    Leoreanu-Fotea, V., Davvaz, B.: Fuzzy hyperrings. Fuzzy Sets and Systems, 160, 2366–2378 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Leoreanu-Fotea, V.: Fuzzy hypermodules. Comput. Math. Appl., 57, 466–475 (2009)MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Zhan, J., Davvaz, B., Shum, K. P.: A new view of fuzzy hypermodules. Acta Mathematica Sinica, English Series, 23, 1345–1356 (2007)MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    Zhan, J., Davvaz, B., Shum, K. P.: A new view of fuzzy hyperquasigroups. J. Intell. Fuzzy Systems, 20, 147–157 (2009)MATHGoogle Scholar
  19. [19]
    Davvaz, B.: On fuzzy relations and fuzzy subhypergroups. Pure Math. Appl., 11, 51–58 (2000)MathSciNetMATHGoogle Scholar
  20. [20]
    Lai, H. L., Zhang, D. X.: Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems, 157, 1865–1885 (2006)MathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    Yu, B. J., Li, Y.: A construction of weakly inverse semigroups. Acta Mathematica Sinica, English Series, 25, 759–784 (2009)MathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    Migliorato, R.: On the complete hypergroups. Riv. Math. Pura Appl., 14, 21–31 (1994)MathSciNetMATHGoogle Scholar
  23. [23]
    Cristea, I.: On the fuzzy subhypergroups of some particular complete hypergroups (I). World Appl. Sci. J., 7(AM), 57–63 (2009)Google Scholar
  24. [24]
    Cristea, I.: On the fuzzy subhypergroups of some particular complete hypergroups (II). In: Proc. Tenth Internat. Congress on Algebraic Hyperstructures and Applications, 2008, Brno, Czech Republic, University of Defence, Brno, 2009, 141–149Google Scholar
  25. [25]
    Cristea, I.: About the fuzzy grade of the direct product of two hypergroupoids. Iran. J. Fuzzy Syst., 7(2), 95–108 (2010)MathSciNetMATHGoogle Scholar
  26. [26]
    Davvaz, B., Karimian, M.: On the γ n-complete hypergroups and K H-hypergroups. Acta Mathematica Sinica, English Series, 24, 1901–1908 (2008)MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    Corsini, P.: Prolegomena of Hypergroup Theory, Aviani Editore, Italy, 1993MATHGoogle Scholar
  28. [28]
    Vougiouklis, J.: Hyperstructures and Their Representations, Hadronic Press, Inc., 1994Google Scholar
  29. [29]
    Corsini, P.: Mutually associative hypergroupoids. In: Algebraic Hyperstructures and Applications (Prague, 1996), Democritus Univ. Thrace, Alexandroupolis, 1997, 25–33Google Scholar
  30. [30]
    Leoreanu, V.: Weak mutually associative hyperstructures (II). In: Algebraic Hyperstructures and Applications (Alexandroupoli-Orestiada, 2002), Spanidis, Xanthi, 2003, 183–189Google Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Irina Cristea
    • 1
    • 2
  • Morteza Jafarpour
    • 3
  • Seyed Sh. Mousavi
    • 4
  1. 1.School of Applied SciencesUniversity of Nova GoricaNova GoricaSlovenia
  2. 2.Department of Civil Engineering and ArchitectureUniversity of UdineUdineItaly
  3. 3.Mathematics DepartmentVali-e-Asr University of RafsanjanRafsanjanIran
  4. 4.Mathematics DepartmentShahid Bahonar University of KermanKermanIran

Personalised recommendations