Geodesic
Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices
Kybernetika, Tome 60 (2024) no. 5, pp. 682-689 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.14736/kyb-2024-5-0682
Classification : 03E72, 03G12
Keywords: quantum logic; s-map; fuzzy relations 
@article{10_14736_kyb_2024_5_0682,
     author = {Isaks, Reinis},
     title = {Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices},
     journal = {Kybernetika},
     pages = {682--689},
     year = {2024},
     volume = {60},
     number = {5},
     doi = {10.14736/kyb-2024-5-0682},
     mrnumber = {4848306},
     zbl = {07980817},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-5-0682/}
}
TY  - JOUR
AU  - Isaks, Reinis
TI  - Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices
JO  - Kybernetika
PY  - 2024
SP  - 682
EP  - 689
VL  - 60
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-5-0682/
DO  - 10.14736/kyb-2024-5-0682
LA  - en
ID  - 10_14736_kyb_2024_5_0682
ER  - 
%0 Journal Article
%A Isaks, Reinis
%T Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices
%J Kybernetika
%D 2024
%P 682-689
%V 60
%N 5
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-5-0682/
%R 10.14736/kyb-2024-5-0682
%G en
%F 10_14736_kyb_2024_5_0682
Isaks, Reinis. Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices. Kybernetika, Tome 60 (2024) no. 5, pp. 682-689. doi: 10.14736/kyb-2024-5-0682

Cité par Sources :