| Title:
|
Bell-type inequalities for parametric families of triangular norms (English) |
| Author:
|
Janssens, Saskia |
| Author:
|
De Baets, Bernard |
| Author:
|
De Meyer, Hans |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
[89]-106 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Bell inequality |
| Keyword:
|
fuzzy set |
| Keyword:
|
quasi-copula |
| Keyword:
|
triangular norm |
| MSC:
|
03E72 |
| MSC:
|
06F05 |
| MSC:
|
54A25 |
| MSC:
|
54A40 |
| idZBL:
|
Zbl 1249.54015 |
| idMR:
|
MR2068600 |
| . |
| Date available:
|
2009-09-24T19:59:39Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135580 |
| . |
| Reference:
|
[1] Bell J. S.: On the Einstein–Podolsky–Rosen paradox.Physics 1 (1964), 195–200 |
| Reference:
|
[2] Genest C., Molina L., Lallena, L., Sempi C.: A characterization of quasi-copulas.J. Multivariate Anal. 69 (1999), 193–205 Zbl 0935.62059, MR 1703371, 10.1006/jmva.1998.1809 |
| Reference:
|
[3] Janssens S., Baets, B. De, Meyer H. De: Bell-type inequalities for commutative quasi-copulas.Fuzzy Sets and Systems, submitted |
| Reference:
|
[4] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
| Reference:
|
[5] Ling C. M.: Representation of associative functions.Publ. Math. Debrecen 12 (1965), 189–212 MR 0190575 |
| Reference:
|
[6] Nelsen R.: An Introduction to Copulas.(Lecture Notes in Statistics 139.) Springer–Verlag, Berlin 1999 Zbl 1152.62030, MR 1653203, 10.1007/978-1-4757-3076-0 |
| Reference:
|
[7] Pitowsky I.: Quantum Probability – Quantum Logic.(Lecture Notes in Physics 321.) Springer–Verlag, Berlin 1989 Zbl 0668.60096, MR 0984603 |
| Reference:
|
[8] Pykacz J., D’Hooghe B.: Bell-type inequalities in fuzzy probability calculus.Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 9 (2001), 263–275 Zbl 1113.03344, MR 1821994, 10.1142/S021848850100079X |
| . |
