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Normal MP-Filters of R 0-Algebras

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Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 54))

Abstract

The aim of this paper is to introduce the notion of normal MP-filters and investigate the structure of R 0-algebras. The relations between normal MP-filters and MP-filters, and between normal MP-filters and filters are discussed. The extension property of normal MP-filters is established. The characteristic properties of normal MP-filters are obtained. Finally, normal R 0-algebras are completely characterized via the normal MP-filters.

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References

  1. Balbes, R., Dwinger, P.: Distributive Lattices. Univ. of Missouri Press, Columbia (1974)

    MATH  Google Scholar 

  2. Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers, Dordrecht (2000)

    MATH  Google Scholar 

  3. Esteva, F., Godo, J.: Monoidal t-norm-based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124, 271–288 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Flondor, P., Georgescu, G., Iorgulescu, A.: Pseudo-t-norms and pseudo-BL algebras. Soft Computing 5(5), 355–371 (2001)

    Article  MATH  Google Scholar 

  5. Georgescu, G., Iorgulescu, A.: Pseudo-BL algebras: A noncommutative extension of BL algebras. In: Abstracts of The Fifth International Conference FSTA 2000, Slovakia (2000)

    Google Scholar 

  6. Hajek, P.: Fleas and fuzzy logic. J. of Mult.-Valued Logic & Soft Computing 11(1-2), 137–152 (2005)

    MATH  MathSciNet  Google Scholar 

  7. Iorgulescu, A.: Some direct ascendents of Wajsberg and MV algebras. Scientiae Mathematicae Japonicae 57, 583–647 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Liu, Y.L., Liu, S.Y.: Normal R 0-algebras. Advances in Systems Science and Applications 4, 665–669 (2004)

    Google Scholar 

  9. Liu, Y.L., Meng, J.: Fuzzy ideals in BCI-algebras. Fuzzy Sets and Systems 123, 227–237 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu, Y.L., Xu, Y., Meng, J.: BCI-implicative ideals of BCI-algebras. Information Sciences 177, 4987–4996 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Liu, Y.L., Xu, Y., Qin, K.Y., Liu, S.Y.: ILI-ideals and prime LI-ideals in lattice implication algebras. Information Sciences 155, 157–175 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Liu, Y.L., Liu, S.Y., Xu, Y.: Pseudo-BCK algebras and PD-posets. Soft Computing 11(1), 91–101 (2007)

    Article  MATH  Google Scholar 

  13. Liu, Y.L., Liu, S.Y., Xu, Y.: An answer to the Jun-Shim-Lele’s open problem on the fuzzy filters. J. Appl. Math. Computing 21, 325–329 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Pei, D.W.: On equivalent forms of fuzzy logic systems NM and IMTL. Fuzzy Sets and Systems 138, 187–195 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wang, G.J.: Non-classical Mathematical Logic and Approximate Reasoning. Science Press, Bei**g (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Wuyi University, Wuyishan, Fujian, 354300, P.R. China

    Yong-lin Liu & Mei-ying Ren

Authors
  1. Yong-lin Liu
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  2. Mei-ying Ren
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Editor information

Editors and Affiliations

  1. Guangzhou Higher Education Mega Center, Guangzhou University, 230Wai Huan ** Road, 510006, China

    Bing-yuan Cao

  2. Department of Mathematics, Hainan Normal University, Haikou, 571158, Hainan, P.R. China

    Cheng-yi Zhang

  3. Department of Electronic Information Engineering, Chongqing University of Science & Technology, 401331, Chongqing

    Tai-fu Li

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© 2009 Springer-Verlag Berlin Heidelberg

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Liu, Yl., Ren, My. (2009). Normal MP-Filters of R 0-Algebras. In: Cao, By., Zhang, Cy., Li, Tf. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88914-4_15

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  • DOI: https://doi.org/10.1007/978-3-540-88914-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88913-7

  • Online ISBN: 978-3-540-88914-4

  • eBook Packages: EngineeringEngineering (R0)

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