| Title:
|
Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices (English) |
| Author:
|
Isaks, Reinis |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
60 |
| Issue:
|
5 |
| Year:
|
2024 |
| Pages:
|
682-689 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A quantum logic is one of possible mathematical models for non-compatible random events. In this work we solve a problem proposed at the conference FSTA 2006. Namely, it is proved that s-maps are symmetric fuzzy relations on a set of all symmetric and idempotent binary matrices. Consequently s-maps are not antisymmetric fuzzy relations. This paper also explores other properties of s-maps, j-maps and d-maps. Specifically, it is proved that s-maps are neither reflexive, nor irreflexive, and nor transitive, j-maps have the same properties as s-maps and d-maps are reflexive and not transitive. (English) |
| Keyword:
|
quantum logic |
| Keyword:
|
s-map |
| Keyword:
|
fuzzy relations |
| MSC:
|
03E72 |
| MSC:
|
03G12 |
| DOI:
|
10.14736/kyb-2024-5-0682 |
| . |
| Date available:
|
2025-01-02T15:51:49Z |
| Last updated:
|
2025-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152720 |
| . |
| Reference:
|
[1] Al-Adilee, M. A., Nánásiová, O.: Copula and s-map on a quantum logic..Inform. Sci. 24 (2009), 4199-4207. MR 2722377, |
| Reference:
|
[2] Lostaks, A.: L-sets and L-valued structures..Nr. 2. University of Latvia, 2003. |
| Reference:
|
[3] Mesiar, R., Klement, E. P.: Open problems posed at the eighth international conference on fuzzy set theory and applications..Kybernetika 42 (2006), 2, 225-235. MR 2241786 |
| Reference:
|
[4] Nánásiová, O., Valášková, Á.: Maps on a quantum logic..Soft Computing 14 (2010), 1047-1052. MR 2722377, |
| Reference:
|
[5] Nánásiová, 0., Pulmannová, S.: S-map and tracial states..Inform. Sci. 5 (2009), 515-520. MR 2490191, |
| . |
