Bell-type inequalities for parametric families of triangular norms

Saskia Janssens; Bernard De Baets; Hans De Meyer

Kybernetika (2004)

  • Volume: 40, Issue: 1, page [89]-106
  • ISSN: 0023-5954

Abstract

top
In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities; second, for the most important parametric families of continuous Archimedean t-norms and each of the inequalities, we identify the parameter values such that the corresponding t-norms satisfy the inequality considered.

How to cite

top

Janssens, Saskia, De Baets, Bernard, and De Meyer, Hans. "Bell-type inequalities for parametric families of triangular norms." Kybernetika 40.1 (2004): [89]-106. <http://eudml.org/doc/33687>.

@article{Janssens2004,
abstract = {In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities; second, for the most important parametric families of continuous Archimedean t-norms and each of the inequalities, we identify the parameter values such that the corresponding t-norms satisfy the inequality considered.},
author = {Janssens, Saskia, De Baets, Bernard, De Meyer, Hans},
journal = {Kybernetika},
keywords = {Bell inequality; fuzzy set; quasi-copula; triangular norm; Bell inequality; fuzzy set; quasi-copula; triangular norm},
language = {eng},
number = {1},
pages = {[89]-106},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bell-type inequalities for parametric families of triangular norms},
url = {http://eudml.org/doc/33687},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Janssens, Saskia
AU - De Baets, Bernard
AU - De Meyer, Hans
TI - Bell-type inequalities for parametric families of triangular norms
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 1
SP - [89]
EP - 106
AB - In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities; second, for the most important parametric families of continuous Archimedean t-norms and each of the inequalities, we identify the parameter values such that the corresponding t-norms satisfy the inequality considered.
LA - eng
KW - Bell inequality; fuzzy set; quasi-copula; triangular norm; Bell inequality; fuzzy set; quasi-copula; triangular norm
UR - http://eudml.org/doc/33687
ER -

References

top
  1. Bell J. S., On the Einstein–Podolsky–Rosen paradox, Physics 1 (1964), 195–200 (1964) 
  2. Genest C., Molina L., Lallena, L., Sempi C., 10.1006/jmva.1998.1809, J. Multivariate Anal. 69 (1999), 193–205 (1999) Zbl0935.62059MR1703371DOI10.1006/jmva.1998.1809
  3. Janssens S., Baets, B. De, Meyer H. De, Bell-type inequalities for commutative quasi-copulas, Fuzzy Sets and Systems, submitted 
  4. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer, Dordrecht 2000 Zbl1087.20041MR1790096
  5. Ling C. M., Representation of associative functions, Publ. Math. Debrecen 12 (1965), 189–212 (1965) MR0190575
  6. Nelsen R., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics 139.) Springer–Verlag, Berlin 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
  7. Pitowsky I., Quantum Probability – Quantum Logic, (Lecture Notes in Physics 321.) Springer–Verlag, Berlin 1989 Zbl0668.60096MR0984603
  8. Pykacz J., D’Hooghe B., 10.1142/S021848850100079X, Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 9 (2001), 263–275 Zbl1113.03344MR1821994DOI10.1142/S021848850100079X

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.