Soft Computing

, Volume 21, Issue 8, pp 1913–1922 | Cite as

Fuzzy prime and maximal filters of residuated lattices

Foundations

Abstract

In this paper, given a residuated lattice M and a lattice L, we introduce the notions of L-fuzzy filter of M, L-fuzzy prime (and maximal) filter of M and give some characterizations of theses notions.

Keywords

Fuzzy filter Fuzzy prime filter Fuzzy maximal filter 

References

  1. Bakhshi M (2011) Fuzzy Boolean and prime filters in non-commutative residuated lattices. In: Proceedings of the 11th Conference on fuzzy systems, pp 159–166, Sistan and Baluchestan UniversityGoogle Scholar
  2. Bakhshi M (2013) Spectrum topology of a residuated lattice. Fuzzy Inf Eng 5:159–172Google Scholar
  3. Ciungu LC (2006) Classes of residuated lattices. Ann Univ Craiova Math Comput Sci Ser 33:189–207. ISSN: 1223-6934Google Scholar
  4. Jipsen P, Tsinakis C (2002) A survey of residuated lattices. In: Martinez J (ed) Ordered algebraic structures. Kluwer Acad. Publ., Dordrecht, pp 19–56Google Scholar
  5. Jun YB, Xu Y, Zhang XH (2005) Fuzzy filters of MTL-algebras. Inf Sci 175:120–138MathSciNetCrossRefMATHGoogle Scholar
  6. Kadji A, Lele C, Tonga M Some classes of pseudo-residuated lattices. Afr Mat. doi:10.1007/s13370-016-0401-8
  7. Liu L, Li K (2005) Fuzzy filters of BL-algebras. Inf Sci 173:141–154MathSciNetCrossRefMATHGoogle Scholar
  8. Swamy UM, Swamy KL (1988) Fuzzy prime ideals of rings. J Math Anal Appl 134:94–103MathSciNetCrossRefMATHGoogle Scholar
  9. Tonga M (2011) Maximality on fuzzy filters of lattices. Afr Mat 22:105–114. doi:10.1007/s13370-011-0009-y MathSciNetCrossRefMATHGoogle Scholar
  10. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Yaounde 1YaoundeCameroon
  2. 2.Department of MathematicsUniversity of DschangDschangCameroon

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