Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices

Reinis Isaks

Kybernetika (2024)

  • Volume: 60, Issue: 5, page 682-689
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Isaks, Reinis. "Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices." Kybernetika 60.5 (2024): 682-689. <http://eudml.org/doc/299868>.

@article{Isaks2024,
abstract = {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.},
author = {Isaks, Reinis},
journal = {Kybernetika},
keywords = {quantum logic; s-map; fuzzy relations},
language = {eng},
number = {5},
pages = {682-689},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices},
url = {http://eudml.org/doc/299868},
volume = {60},
year = {2024},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 5
SP - 682
EP - 689
AB - 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.
LA - eng
KW - quantum logic; s-map; fuzzy relations
UR - http://eudml.org/doc/299868
ER -

References

top
  1. Al-Adilee, M. A., Nánásiová, O., , Inform. Sci. 24 (2009), 4199-4207. MR2722377DOI
  2. Lostaks, A., L-sets and L-valued structures., Nr. 2. University of Latvia, 2003. 
  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. MR2241786
  4. Nánásiová, O., Valášková, Á., , Soft Computing 14 (2010), 1047-1052. MR2722377DOI
  5. Nánásiová, 0., Pulmannová, S., , Inform. Sci. 5 (2009), 515-520. MR2490191DOI

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.