Skip to main content
SpringerLink
Log in

Very true operators in effect algebras

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

We introduce the concept of very true operator on an effect algebra. Although an effect algebra is only partial, we define it in the way which is in accordance with traditional definitions in residuated lattices or basic algebras. This is possible if we require monotonicity as an additional condition. We prove that very true operators on effect algebras can be characterized by means of certain subsets which are conditionally complete.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Bělohlávek R, Vychodil V (2005) Reducing the size of fuzzy concept lattices by hedges. In: FUZZ-IEEE 2005, the IEEE international conference on fuzzy systems, Reno, NV, USA, pp 663–668

  • Botur M, Chajda I, Halaš R (2010) Are basic algebras residuated structures?. Soft Comput 14:251–255

    Article  MATH  Google Scholar 

  • Chajda I (2011) Hedges and successors in basic algebras. Soft Comput 15:613–618

    Article  MATH  Google Scholar 

  • Chajda I, Halaš R (2011) Effect algebras are conditionally residuated structures. Soft Comput 15:1383–1387

    Article  MATH  Google Scholar 

  • Chajda I, Halaš R, Kühr J (2009) Every effect algebra can be made into a total algebra. Algebra Universalis 61:139–150

    Article  MathSciNet  MATH  Google Scholar 

  • Dvurečenskij A, Pulmannová S (2000) New trends in quantum structures. Kluwer, Dordrecht; Ister Science, Bratislava

  • Foulis DJ, Bennett MK (1994) Effect algebras and unsharp quantum logics. Found Phys 24:1325–1346

    Article  MathSciNet  Google Scholar 

  • Hájek P (2001) On very true. Fuzzy Sets Syst 124:329–333

    Article  MATH  Google Scholar 

  • Zadeh LA (1972) A fuzzy-set-theoretical interpretation of linguistic hedges. J Cybern 2:4–34

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The work of the first author is supported by the project Algebraic Methods in Quantum Structures, No. CZ.1.07/2.3.00/20.0051.

Author information

Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Ivan Chajda

  2. Department of Computer Science, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Miroslav Kolařík

Authors
  1. Ivan Chajda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miroslav Kolařík
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivan Chajda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chajda, I., Kolařík, M. Very true operators in effect algebras. Soft Comput 16, 1213–1218 (2012). https://doi.org/10.1007/s00500-012-0807-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-012-0807-7

Keywords

Search

Navigation