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Lattice structure on some fuzzy algebraic systems

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Abstract

In this paper, we study the lattice structure of some fuzzy algebraic systems such as (G-)fuzzy groups, some fuzzy ordered algebras and fuzzy hyperstructures. We prove that under suitable conditions, these structures form a distributive or modular lattice.

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References

  • Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. Kluwer, Netherlands

    MATH  Google Scholar 

  • Dudek WA (1992) On proper BCC-algebras. Bull Inst Math Acad Sin 20(2) June

  • Dudek WA (2000) Algebras inspired by logics. Math Stud (LVOV) 14:5–18

    MathSciNet  Google Scholar 

  • Dudek WA, Jun YB (1999) Fuzzy BCC-ideals in BCC-algebras. Math Montisnigri (10):21–30

    MATH  MathSciNet  Google Scholar 

  • Dudek WA, Zhang X (1998) On ideals and congruences in BCC-algebras. Czech Math J 48(123):21–29

    Article  MATH  MathSciNet  Google Scholar 

  • Dudek WA, Jun YB, Stojakovi Z (2001) On fuzzy ideals in BCC-algebras. Fuzzy Sets Syst 123(2):251–258

    Article  MATH  Google Scholar 

  • Imai Y, Iséki K (1966) On axiom systems of propositional calculi XIV. Proc Jpn Acad 42:19–22

    Article  MATH  Google Scholar 

  • Jun YB, Xin XL (2001) Fuzzy hyper BCK-ideals of hyper BCK-algebras. Sci Math Japonicae 53(2):353–360

    MATH  MathSciNet  Google Scholar 

  • Jun YB, Zahedi MM, Xin XL, Borzooei RA (2000) On hyper BCK-algebras. Ital J Pure Appl Math 10:127–136

    MathSciNet  Google Scholar 

  • Komori Y (1984) The class of BCC-algebras is not a variety. Math Jpn 29:391–394

    MATH  MathSciNet  Google Scholar 

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

  • Meng J, Jun YB (1994) BCK-algebras. Kyung Moon Sa Co., Seoul, South Korea

  • Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35:512–517

    Article  MATH  MathSciNet  Google Scholar 

  • Soleimaninasab A, Mashinchi M (2004) Generalizes groups. In: Proceedings of the 5th Iranian conference on fuzzy systems. Imam Hosein University, Tehran, Iran, pp 7–9 September

  • Thomas KV (1997) Fuzzy sets and their application in algebra. Ph.D thesis, University of Delhi, India

  • Zahedi MM, Hasankhani A (1996) F-polygroups (II). Inf Sci 89:225–243

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei

  2. Department of Mathematics, Bojnord University, Bojnord, Iran

    M. Bakhshi

  3. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    M. Mashinchi

Authors
  1. R. A. Borzooei
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  2. M. Bakhshi
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  3. M. Mashinchi
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Corresponding author

Correspondence to R. A. Borzooei.

Additional information

This research partially is supported by the “ Fuzzy Systems and its Applications Center of Excelence, Shahid Bahonar University of Kerman, Iran”.

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Borzooei, R.A., Bakhshi, M. & Mashinchi, M. Lattice structure on some fuzzy algebraic systems. Soft Comput 12, 739–749 (2008). https://doi.org/10.1007/s00500-007-0232-5

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  • DOI: https://doi.org/10.1007/s00500-007-0232-5

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