Kybernetika 60 no. 5, 682-689, 2024

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

Reinis IsaksDOI: 10.14736/kyb-2024-5-0682

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.

Keywords:

fuzzy relations, s-map, quantum logic

Classification:

03E72, 03G12

paper.pdf

References:

  1. A. M. Al-Adilee and O. Nánásiová: Copula and s-map on a quantum logic. Inform. Sci. 24 (2009), 4199-4207.   DOI:10.1016/j.ins.2009.08.011
  2. A. Šostak: L-sets and L-valued structures. Nr. 2. University of Latvia, 2003.   CrossRef
  3. R. Mesiar and E. P. Klement: Open problems posed at the eighth international conference on fuzzy set theory and applications. Kybernetika 42 (2006), 2, 225-235.   CrossRef
  4. O. Nánásiová and {L}. Valášková: Maps on a quantum logic. Soft Computing 14 (2010), 1047-1052.   DOI:10.1007/s00500-009-0483-4
  5. O. Nánásiová and S. Pulmannová: S-map and tracial states. Inform. Sci. 5 (2009), 515-520.   DOI:10.1016/j.ins.2008.07.032