Skip to main content
SpringerLink
Log in
Book cover

Quantitative Logic and Soft Computing 2016 pp 415–428Cite as

Hyper Equality Algebras

  • Conference paper
  • First Online:

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

Abstract

In this paper, we introduce a new structure, called hyper equality algebras which are a generalization of equality algebras, and investigate some related properties. Then we define (weak, strong) hyper filters and (weak, strong) hyper deductive systems, and give relations between them. Moreover we discuss relations between hyper equality algebras and other hyper structures, such as hyper EQ-algebras, hyper BCK-algebras and weak hyper residuated lattices. Finally, we also obtain quotient hyper equality algebras via regular hyper congruence relations.

This is a preview of subscription content, 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

Learn about institutional subscriptions

References

  1. Nov\(\acute{a}\)k, V., Baets, B.D.: EQ-algebras. Fuzzy Sets Syst. 160, 2956–2978 (2009)

    Google Scholar 

  2. Jenei, S.: Equality algebras. Stud. Log. 100, 1201–1209 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Marty, F.: Surune generalization de la notion de group. The 8th Congress Math. Scandinaves, Stockholm, pp. 45–49 (1934)

    Google Scholar 

  4. Borzooei, R.A., Bakhshi, M., Zahiri, O.: Filter theory on hyper residuated lattice. Quasigroups Relat. Syst. 22, 33–50 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Borzooei, R.A., Hasankhani, A., Zahedi, M.M., JUN, Y.B.: On hyper K-algebras. Math. Japonicae 52, 113–121 (2000)

    MathSciNet  Google Scholar 

  6. Borzooei, R.A., Niazian, S.: Weak hyper residuated lattics. Quasigroups Relat. Syst. 21, 29–42 (2013)

    MathSciNet  MATH  Google Scholar 

  7. Ghorbani, S., Hasankhani, A., Eslami, E.: Hyper MV-algebras. Set-Valued Math. Appl. 1, 205–222 (2008)

    MATH  Google Scholar 

  8. Jun, Y.B., Zahedi, M.M., Xin, X.L., Borzooei, R.A.: On hyper BCK-algebras. Italian J. Pure Appl. Mathematics-N 8, 127–136 (2000)

    MathSciNet  MATH  Google Scholar 

  9. Xin, X.L.: Hyper BCI-algebras. Discuss. Math. General Algebra Appl. 26, 5–19 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Borzooei, R.A., Saffar, B.G., Ameri, R.: On hyper EQ-algebras. Italian J. Pure Appl. Mathematics-N. 31, 77–96 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Cheng, X.Y., Xin, X.L.: Filter theory On hyper BE-algebras. Italian J. Pure Appl. Mathematics-N. 35, 509–526 (2015)

    MathSciNet  MATH  Google Scholar 

  12. Cheng, X.Y., Xin, X.L.: Deductive systems in hyper EQ-algebras. J. Math. Res. Appl. (submitted)

    Google Scholar 

Download references

Acknowledgments

This research is supported by a grant of National Natural Science Foundation of China (11571281).

Author information

Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, People’s Republic of China

    Xiao-Yun Cheng & Xiao-Long Xin

  2. General Education Center, Xi’an Peihua University, Xi’an, 710065, China

    Xiao-Yun Cheng

  3. Department of Mathematics Education, Gyeongsang National University, Chinju, 660-701, Korea

    Young-Bae Jun

Authors
  1. Xiao-Yun Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Long Xin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Young-Bae Jun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Long Xin .

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

Cheng, XY., Xin, XL., Jun, YB. (2017). Hyper Equality Algebras. 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_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46206-6_40

  • 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