Skip to main content
SpringerLink
Log in

Parametrization Filters and Their Properties in Residuated Lattices

  • Conference paper
  • First Online:
Quantitative Logic and Soft Computing 2016

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 510))

  • 542 Accesses

Abstract

Filters play a key role in studying algebraic structures of logics. Recently, various special filters in residuated lattices have been introduced. Hence it is very important to develop a general definition for special filters. In the paper, we introduce the notion of parametrization filters and study some of their properties. The relationship of Extension property (Triple of equivalent characteristics, and Quotient characteristics) between the set of parametrization filters and the set of \((\alpha ,\beta ]\)-fuzzy parametrization filters is investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Blount, K., Tsinakis, C.: The structure of residuated lattices. Int. J. Algebra Comput. 13, 437–461 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Liu, L.Z.: Generalized intuitionistic fuzzy filters on residuated lattices. J. Intell. Fuzzy Syst. 28, 1545–1552 (2015)

    MathSciNet  Google Scholar 

  3. Liu, L.Z., Li, K.T.: Fuzzy filters of BL-algebras. Inform. Sci. 173, 141–154 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Liu, L.Z., Li, K.T.: Fuzzy Boolean and positive implicative filters of BL-algebras. Fuzzy Sets Syst. 152, 333–348 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu, L.Z., Zhang, X.Y.: Applications of transfer principle to fuzzy theory with thresholds \((\alpha , \beta )\). In: Proceedings of International Conference on Quantitative Logic and Quantification of Software. pp. 125–129 (2009)

    Google Scholar 

  6. Ma, X.L., Zhan, J.M., Dudek, W.A.: Some kinds of \((\bar{\in }, \bar{\in }\vee \bar{q})\)-fuzzy filters of BL-algebras. Comput. Math. Appl. 58, 248–256 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ma, Z.M.: Lattices of (generalized) fuzzy filters in residuated lattices. J. Intell. Fuzzy Syst. 27, 2281–2287 (2014)

    MathSciNet  MATH  Google Scholar 

  8. Rachůnek, J., Šalounova, D.: Fuzzy filters and fuzzy prime filters of bounded \(RL\)-monoids and pseudo BL-algebras. Inform. Sci. 178, 3474–3481 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Swamy, U.M., Viswanadha Raju, D.: Algebraic fuzzy systems. Fuzzy Sets Syst. 41, 187–194 (1991)

    Google Scholar 

  10. Víta, M.: Fuzzy t-filters and their properties. Fuzzy Sets Syst. 247, 127–134 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Víta, M.: Why are papers about filters on residuated structures (usually) trivial? Inform. Sci. 276, 387–391 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. van Alten, C.J.: Representable Biresiduated Lattices. J. Algebra. 247, 672–691 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xiao, L., Liu, L.Z.: A note on some filters in residuated lattices. J. Intell. Fuzzy Syst. 30, 493–500 (2016)

    Article  MathSciNet  Google Scholar 

  14. Yuan, X.H., Zhang, C., Ren, Y.H.: Generalized fuzzy groups and many-valued implications. Fuzzy Sets Syst. 138, 205–211 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang, H.R., Li, Q.G.: \((\in, \in \vee q)\)-fuzzy t-filters on residuated lattices. J. Intell. Fuzzy Syst. 29, 1521–1526 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by NSFC (Nos. 60875084, 61273017), by the Fundamental Research Funds for the Central Universities (JUSRP21118, JUSRP211A24), by Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents and the Project-sponsored by SRF for ROCS, SEM.

Author information

Authors and Affiliations

  1. College of Science, Jiangnan University, Wuxi, 214122, China

    Lian-Zhen Liu & Xiang-Yang Zhang

Authors
  1. Lian-Zhen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiang-Yang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lian-Zhen Liu .

Editor information

Editors and Affiliations

  1. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    Tai-He Fan

  2. Fujian, Jimei University Fujian, Xiamen, China

    Shui-Li Chen

  3. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    San-Min Wang

  4. Yanta, Shaanxi Normal University Yanta, Xi’an, China

    Yong-Ming Li

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Cite this paper

Liu, LZ., Zhang, XY. (2017). Parametrization Filters and Their Properties in Residuated Lattices. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46206-6_36

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46205-9

  • Online ISBN: 978-3-319-46206-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation