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Generalized Fuzzy Regular Filters on Residuated Lattices

  • Yi Liu
  • Lianming Mou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9436)

Abstract

The aim of this paper is further to develop the fuzzy filter theory of general residuated lattices. The concepts of \((\in ,\in \vee q_{k})\)-fuzzy positive implicative filter, \((\in ,\in \vee q_{k})\)-fuzzy MV filter and \((\in ,\in \vee q_{k})\)-fuzzy regular filter are introduced; Their properties are investigated, and some equivalent characterizations of these generalized fuzzy filters are also derived.

References

  1. 1.
    Bhakat, S.K., Das, P.: \((\in,\in \vee q)\)-fuzzy subgroups. Fuzzy Sets Syst. 80, 359–368 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bhakat, S.K.: \((\in \vee q)\)-level subset. Fuzzy Sets Syst. 103, 529–533 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Dilworth, R.P., Ward, M.: Residuated lattices. Trans. Am. Math. Soc. 45, 335–354 (1939)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Jun, Y.B., Song, S.Z., Zhan, J.M.: Generalizations of of \((\in, \in \vee q)\)-Fuzzy Filters in \(R_0\) algebras. Int. J. Math. Math. Sci. 2010, 1–19 (2010)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Kondo, M., Dudek, W.A.: Filter theory of BL-algebras. Soft. Comput. 12, 419–423 (2008)zbMATHCrossRefGoogle Scholar
  6. 6.
    Liu, L.Z., Li, K.T.: Fuzzy implicative and Boolean filters of R\(_0\)-algebras. Inform. Sci. 171, 61–71 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Ma, X.L., Zhan, J.M., Jun, Y.B.: On \((\in,\in \vee q)\)-fuzzy filters of R\(_0\)-algebras. Math. Log. Quart. 55, 452–467 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liu, Y., Xu, Y.: Inter-valued \((\alpha, \beta )\)-fuzzy implication subalgebras. Comput. Sci. 38(4), 263–266 (2011)Google Scholar
  9. 9.
    Liu, Y., Xu, Y., Qin, X.Y.: Interval-valued T-fuzzy filters and interval-valued T-fuzzy congruences on residuated lattices. J. Intell. Fuzzy Syst. 26, 2021–2033 (2014)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhu, Y.Q., Xu, Y.: On filter theory of residuated lattices. Inf. Sci. 180, 3614–3632 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Zhu, Y., Zhan, J., Jun, Y.B.: On \((\bar{\in },\bar{\in }\vee \bar{q})\)-fuzzy filters of residuated lattices. In: Cao, B., Wang, G., Chen, S., Guo, S. (eds.) Quantitative Logic and Soft Computing 2010. AISC, vol. 82, pp. 631–640. Springer, Heidelberg (2010) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Data Recovery Key Lab of Sichuan Province, Neijiang Normal UniversityNeijiangPeople’s Republic of China
  2. 2.College of Mathematics and Information Sciences, Neijiang Normal UniversityNeijiangPeople’s Republic of China

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