Skip to main content
SpringerLink
Log in

Finite direct products of EQ-algebras

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The aim of this paper is to improve the filters of EQ-algebras proposed by V. Novák and B. De Baets. We give a new class of EQ-algebras, namely multiplicatively relative EQ-algebras, and investigate their properties. Particularly, following the work “The lattice of prefilters of an EQ-algebra,” we give a characterization of filter generated by a nonempty subset of multiplicatively relative EQ-algebras. In addition, we give the concrete forms of Spec(E) and Max(E) in an EQ-algebra E, which are finite direct products of special types of EQ-algebras.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Belluce LP, Di Nola A, Lettieri A (1992) Subalgebras, direct products and associated lattices of \(MV\)-algebras. Glasgow Math J 34:301–307

    Article  MathSciNet  MATH  Google Scholar 

  • Burris S, Sankappanavar HP (1981) A course in universal algebra, graduate texts in mathematics, vol 78. Springer, New York

    MATH  Google Scholar 

  • Dyba M, EI-Zekey M, Novák V (2016) Non-commutative first-order \(EQ\)-logics. Fuzzy Sets Syst 292:215–241

    Article  MathSciNet  MATH  Google Scholar 

  • El-Zekey M (2010) Representable good \(EQ\)-algebras. Soft Comput 14:1011–1023

    Article  MATH  Google Scholar 

  • El-Zekey M, Novák V, Mesiar R (2011) On good \(EQ\)-algebras. Fuzzy Sets Syst 178:1–23

    Article  MathSciNet  MATH  Google Scholar 

  • Georgescu G, Leuştean L, Mureşan C (2010) Maximal residuated lattices with lifting boolean center. Algebra Univers 63:83–99

    Article  MathSciNet  MATH  Google Scholar 

  • Leuştean L (2004) Representations of many-valued algebras. Ph.D. thesis, University of Bucharest

  • Liu LZ, Zhang XY (2014) Implicative and positive implicative prefilters of \(EQ\)-algebras. J Intell Fuzzy Syst 26:2087–2097

    MathSciNet  MATH  Google Scholar 

  • Mohtashamnia N, Torkzadeh L (2017) The lattice of prefilters of an \(EQ\)-algebra. Fuzzy Sets Syst 311:86–98

    Article  MathSciNet  MATH  Google Scholar 

  • Novák V (2006) EQ-algebras: primary concepts and properties. In: Proceedings of the Czech–Japan seminar, ninth meeting, Kitakyushu and Nagasaki, 18–22 August , Graduate School of Information, Waseda University, pp 219–223

  • Novák V, De Baets B (2009) \(EQ\)-algebras. Fuzzy Sets Syst 160:2956–2978

    Article  MathSciNet  MATH  Google Scholar 

  • Yang J, Xin X L, He P F On topological \(EQ\)-algebras, Iranian Journal of Fuzzy Systems, https://doi.org/10.22111/IJFS.2018.3550.

  • Yang J, Xin XL, He PF (2017) Uniform topology on EQ-algebras. Open Math 15:354–364

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are highly grateful to the editor and anonymous referees for their careful reading and valuable suggestions which helped to improve the paper. This research is supported by a grant of Scientific Research Project of Shaanxi Provincial Department of Education (18JK0407).

Author information

Authors and Affiliations

  1. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Jiang Yang

  2. School of Mathematics and Statistics, Yulin University, Yulin, 719000, China

    Xiongwei Zhang

Authors
  1. Jiang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiongwei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiang Yang.

Ethics declarations

Conflict of Interest

The authors declare that there is no conflict of interests.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Communicated by A. Di Nola.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Zhang, X. Finite direct products of EQ-algebras. Soft Comput 23, 7495–7504 (2019). https://doi.org/10.1007/s00500-018-03687-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-03687-5

Keywords

Search

Navigation