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Nonlinear Mathematics for Uncertainty and its Applications pp 667–674Cite as

L-Fuzzy Subalgebras and L-Fuzzy Filters of R0-Algebras

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

R0-algebras are the logic algebras associated to the formal deductive system L* for fuzzy propositional calculus. In this paper, the concepts of L-fuzzy subalgebras and L-fuzzy filters of R0-algebras are introduced. Properties of L-fuzzy subalgebras and L-fuzzy filters are investigated. characterizations of L-fuzzy subalgebras and L-fuzzy filters of R0-algebras are obtained. It is proved that an L-fuzzy set on an R0-algebra M is an L-fuzzy subalgebra of M if and only if for all t ∈ L, every its nonempty t-level section is a subalgebra of M. It is also proved that under some reasonable conditions, images and inverse images of L-fuzzy subalgebras (resp., L-fuzzy filters) of R0-algebra homomorphisms are still L-fuzzy subalgebras (resp. L-fuzzy filters).

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References

  1. Chang, C.C.: Algebras Analysis of Many-valued Logics. Trans. Amer. Math. Soc. 88, 467–490 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)

    Book  MATH  Google Scholar 

  3. Hoo, C.S.: Fuzzy Implicative and Boolean Ideals of MV-algebras. Fuzzy Sets and Systems 41, 315–327 (1994)

    Article  MathSciNet  Google Scholar 

  4. Hoo, C.S.: Some Fuzzy concepts of BCI, BCK and MV-algebras. Int. J. Approx. Reason 18, 177–189 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu, C.H., Xu, L.S.: MP-filters of Fuzzy Implication Algebras. Fuzzy Systems and Math. 2, 1–6 (2009)

    MATH  Google Scholar 

  6. Liu, L.Z., Li, K.T.: Fuzzy Implicative and Boolean Filters of R0-algebras. Information Sci. 171, 61–71 (2005)

    Article  MATH  Google Scholar 

  7. Liu, L.Z., Li, K.T.: R0-algebras and Weak Dually Residuated Lattice Ordered Semigroups. Czech Math J. 56, 339–348 (2006)

    Article  MATH  Google Scholar 

  8. Liu, L.Z., Zhang, X.Y.: States on R0-algebras. Soft Comput. 12, 1094–1104 (2008)

    Google Scholar 

  9. Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18, 145–174 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pei, D.W., Wang, G.J.: The Completeness and Application of Formal Systems L *. Science in China (Ser. E) 1, 56–64 (2002)

    Google Scholar 

  11. Xu, Y., Qin, K.Y.: On Fuzzy Filters of Lattice Implication algebras. J. Fuzzy Math. 1, 251–260 (1993)

    MathSciNet  MATH  Google Scholar 

  12. Xu, Y., Qin, K.Y.: Fuzzy Lattice Implication Algebras. J. Southweast Jiaotong Univ. 2, 121–127 (1995) (in chinese)

    Google Scholar 

  13. Wang, G.J.: On Logic Foundations of Fuzzy Reasoning. Inform. Sci. 117, 47–88 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, G.J.: Non-Classical Mathematical Logic and Approximate Reasoning. Science in China Press, Beijing (2003) (in chinese)

    Google Scholar 

  15. Zadeh, L.A.: Fuzzy Sets. Information Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Elementary Education, Chifeng College, Chifeng, 024001, Inner Mongolia, P.R. China

    Chunhui Liu

  2. Department of Mathematics, Yangzhou University, Yangzhou, 225002, Jiangsu, P.R. China

    Luoshan Xu

Authors
  1. Chunhui Liu
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  2. Luoshan Xu
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Liu, C., Xu, L. (2011). L-Fuzzy Subalgebras and L-Fuzzy Filters of R0-Algebras. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_81

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_81

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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