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A new view of L-fuzzy polygroups

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Abstract

In this paper, we introduce the concept of (weak) L-fuzzy polygroups and give a theorem to present the connection between the crisp polygroups and L-fuzzy polygroups. We also provide the notion of (normal) L-fuzzy subpolygroups of a (weak) L-fuzzy polygroup and investigate some of their properties. We show that the set of all the normal L-fuzzy subpolygroups is a modular lattice and obtain a kind of weak L-fuzzy quotient polygroup. Moreover, we define two kinds of operators on \({\fancyscript{L}(H)}\), where \({\fancyscript{L}(H)}\) is the set of all the L-fuzzy subsets in a weak L-fuzzy polygroup H, to characterize L-fuzzy subpolygroups and present some related theorems. Finally, we investigate the homomorphism properties of L-fuzzy polygroups.

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References

  1. Ameri R, Hedayati H (2007) On fuzzy closed, invertible and reflexive subsets of hypergroups. Ital J Pure Appl Math 22:95–114

    MathSciNet  MATH  Google Scholar 

  2. Comer SD (1982) Extension of polygroups by polygroups and their representations using colour schemes. In: Universal algebra and lattice theory, Lecture Notes in Meth., vol 1004, pp 91–103

  3. Comer SD (1984) Polygroups derived from cogroups. J Algebra 89:397–405

    Article  MathSciNet  MATH  Google Scholar 

  4. Corsini P (1993) Prolegomena of hypergroup theory. Aviani Editore, Italy

    MATH  Google Scholar 

  5. Corsini P, Leoreanu V (1995) Join spaces associated with fuzzy sets. J Comb Inf Syst Sci 20:293–303

    MathSciNet  MATH  Google Scholar 

  6. Corsini P, Leoreanu V (2002) Fuzzy sets and join spaces associated with rough sets. Rend Circ Mat Palermo 51:527–536

    Article  MathSciNet  MATH  Google Scholar 

  7. Corsini P, Leoreanu V (2003) Applications of hyperstructure theory, advances in mathematics (Dordrecht). Kluwer, Dordrecht

    Google Scholar 

  8. Corsini P, Tofan I (1997) On fuzzy hypergroups. Pure Math Appl 8:29–37

    MathSciNet  MATH  Google Scholar 

  9. Davvaz B (2001) On polygroups and weak polygroups. Southeast Asian Bull Math 25:87–95

    Article  MathSciNet  MATH  Google Scholar 

  10. Davvaz B (2007) Extensions of fuzzy hyperideals in H v -semigroups. Soft Comput 11:829–837

    Article  MATH  Google Scholar 

  11. Davvaz B (2007) Applications of the γ*-relation to polygroups. Comm Algebra 35:2698–2706

    Article  MathSciNet  MATH  Google Scholar 

  12. Davvaz B, Corsini P (2007) Redefined fuzzy H v -submodules and many valued implications. Inf Sci 177:865–875

    Article  MathSciNet  MATH  Google Scholar 

  13. Davvaz B, Poursalavati NS (1999) On polygroup hyperrings and representation of polygroups. J Korean Math Soc 36(6):1021–1031

    MathSciNet  MATH  Google Scholar 

  14. Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18:145–174

    Article  MathSciNet  MATH  Google Scholar 

  15. Kehagias A, Serafimidis K (2005) The L-fuzzy Nakano hypergroup. Inf Sci 169:305–327

    Article  MathSciNet  MATH  Google Scholar 

  16. Leoreanu V (2000) Direct limit and inverse limit of join spaces associated with fuzzy sets. Pure Math Appl 11:509–516

    MathSciNet  MATH  Google Scholar 

  17. Leoreanu V (2009) Fuzzy hypermodules. Comput Math Appl 57:466–475

    Article  MathSciNet  MATH  Google Scholar 

  18. Leoreanu V, Davvaz B (2009) Fuzzy hyperrings. Fuzzy Sets Syst 160:2366–2378

    Article  MATH  Google Scholar 

  19. Marty F (1934) Sur une generalization de la notion de groupe. In: 8th Congress Math. Scandinaves, Stockholm, pp 45–49

  20. Morsi NN, Yakout MM (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Syst 100:327–342

    Article  MathSciNet  MATH  Google Scholar 

  21. Sen MK, Ameri R, Chowdhury G (2008) Fuzzy hypersemigroups. Soft Comput 12:891–900

    Article  MATH  Google Scholar 

  22. Serafimidis K, Kehagias A, Konstantinidou M (2002) The L-fuzzy Corsini join hyperoperation. Ital J Pure Appl Math 12:83–90

    MathSciNet  MATH  Google Scholar 

  23. Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press Inc., Palm Harbor

    MATH  Google Scholar 

  24. Wu WZ, Yee L, Mi JS (2005) On characterizations of \({(\fancyscript{I, T})}\)-fuzzy rough approximation operators. Fuzzy Sets Syst 154:76–102

    Article  MATH  Google Scholar 

  25. Yin Y, Davvaz B, Zhan J (2010) A fuzzy view of \(\Upgamma\)-hyperrings. Neural Comput Appl doi:10.1007/s00521-010-0509-y

  26. Yin Y, Zhan J, Xu D, Wang J (2010) The L-fuzzy hypermodules. Comput Math Appl 59:953–963

    Article  MathSciNet  MATH  Google Scholar 

  27. Yin Y, Zhan J, Corsini P (2011) Fuzzy roughness of n-ary hypergroups based a complete residuated lattice. Neural Comput Applic 20:41–57

    Google Scholar 

  28. Yin Y, Zhan J, Corsini P (2011) L-fuzzy roughness of n-ary polygroups.. Acta Math Sin 27:97–118

    Article  MathSciNet  Google Scholar 

  29. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–358

    Article  MathSciNet  MATH  Google Scholar 

  30. Zahedi MM, Bolurian M, Hasankhani A (1995) On polygroups and fuzzy subpolygroups. J Fuzzy Math 3:1–15

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

We would like to express our warmest thanks to the referees for their interest in our work and their valuable comments for improving the paper. This work was supported by the Natural Science Foundation for Young Scholars of Jiangxi, China (2010GQS0003); the Science Foundation of Education Committee for Young Scholars of Jiangxi, China (GJJ11143); a grant of National Natural Science Foundation of China # 60875034; a grant of the Natural Science Foundation of Education Committee of Hubei Province, China, # D20092901; and also a grant of the Natural Science Foundation of Hubei Province, China # 2009CDB340.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, East China Institute of Technology, 344000, Fuzhou, Jiangxi, China

    Yunqiang Yin

  2. Department of Mathematics, Hubei University for Nationalities, 445000, Enshi, Hubei Province, China

    Jianming Zhan

  3. Department of Mathematics, Honghe University, 661100, Mengzi, Yunnan, China

    Xiaokun Huang

Authors
  1. Yunqiang Yin
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  2. Jianming Zhan
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  3. Xiaokun Huang
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Correspondence to Yunqiang Yin.

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Yin, Y., Zhan, J. & Huang, X. A new view of L-fuzzy polygroups. Neural Comput & Applic 20, 589–602 (2011). https://doi.org/10.1007/s00521-011-0555-0

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