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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
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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 
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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

[1] Al-Adilee, M. A., Nánásiová, O.: Copula and s-map on a quantum logic. Inform. Sci. 24 (2009), 4199-4207. | DOI | MR

[2] Šostak, 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. | MR

[4] Nánásiová, O., Valášková, Á.: Maps on a quantum logic. Soft Computing 14 (2010), 1047-1052. | DOI | MR

[5] Nánásiová, O., Pulmannová, S.: S-map and tracial states. Inform. Sci. 5 (2009), 515-520. | DOI | MR

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