Skip to main content
SpringerLink
Log in

Fuzzy Primeness in Quantales

  • Chapter
  • First Online:
Decision Making under Constraints

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 276))

  • 412 Accesses

Abstract

This paper is an investigation about primeness in quantales environment. It is proposed a new definition for prime ideal in noncommutative setting. As a consequence, fuzzy primeness can be defined in similar way to ring theory.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. Yang, L., Luoshan, X.: Roughness in quantales. Inf. Sci. 220, 568–579 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Luo, Q., Wang, G.: Roughness and fuzziness in quantales. Inf. Sci. 271, 14–30 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Navarro, G., Cortadellas, O., Lobillo, F.J.: Prime fuzzy ideals over noncommutative rings. Fuzzy Sets Syst. 199(0):108–120 (2012)

    Google Scholar 

  4. Handelman, D., Lawrence, J.: Strongly prime rings. Trans. Am. Math. Soc. 211, 209–223 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bergamaschi, F.B., Santiago, R.H.N.: Strongly prime fuzzy ideals over noncommutative rings. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–5 (2013)

    Google Scholar 

  6. Bergamaschi, F.B., Santiago, R.H.N.: A fuzzy version of uniformly strongly prime ideals. In: 2014 IEEE Conference on Norbert Wiener in the 21st Century (21CW), pp. 1–6. IEEE (2014)

    Google Scholar 

  7. Rosenthal, K.I.: Quantales and Their Applications, vol. 234. Longman Scientific & Technical Harlow (1990)

    Google Scholar 

  8. Olson, D.M.: A uniformly strongly prime radical. J. Austral. Math. Soc. (Ser. A) 43, 95–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  10. Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl. 35(3), 512–517 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang jin Liu: Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets Syst. 8(2), 133–139 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang-jin, L.: Operations on fuzzy ideals. Fuzzy Sets Syst. 11(13), 19–29 (1983)

    MathSciNet  MATH  Google Scholar 

  13. Mukherjee, T.K., Sen, M.K.: On fuzzy ideals of a ring. Fuzzy Sets Syst. 21(1), 99–104 (1987)

    Article  MATH  Google Scholar 

  14. Swamy, U.M., Swamy, K.L.N.: Fuzzy prime ideals of rings. J. Math. Anal. Appl. 134(1), 94–103 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yue, Z.: Prime l-fuzzy ideals and primary l-fuzzy ideals. Fuzzy Sets Syst. 27(3), 345–350 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kumar, R.: Fuzzy semiprimary ideals of rings. Fuzzy Sets Syst. 42(2), 263–272 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kumar, R.: Fuzzy nil radicals and fuzzy primary ideals. Fuzzy Sets Syst. 43(1), 81–93 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kumbhojkar, H.V., Bapat, M.S.: Not-so-fuzzy fuzzy ideals. Fuzzy Sets Syst. 37(2), 237–243 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kumbhojkar, H.V., Bapat, M.S.: On prime and primary fuzzy ideals and their radicals. Fuzzy Sets Syst. 53(2), 203–216 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank UESB (Southwest Bahia State University) and UFRN (Federal University of Rio Grande do Norte) for their financial support. This research was partially supported by the Brazilian Research Council (CNPq) under the process 306876/2012-4.

Author information

Authors and Affiliations

  1. Southwest Bahia State University, Vitória da Conquista, Brazil

    Flaulles Boone Bergamaschi

  2. Federal University of Rio Grande do Norte, Natal, Brazil

    Regivan H. N. Santiago

Authors
  1. Flaulles Boone Bergamaschi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Regivan H. N. Santiago
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Flaulles Boone Bergamaschi .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bergamaschi, F.B., Santiago, R.H.N. (2020). Fuzzy Primeness in Quantales. In: Ceberio, M., Kreinovich, V. (eds) Decision Making under Constraints. Studies in Systems, Decision and Control, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-030-40814-5_4

Download citation

Publish with us

Policies and ethics

Search

Navigation