Quasiorders, Tolerance Relations and Corresponding “Partitions”

• Autorzy: Marek Nowak
• Języki publikacji: EN

Abstrakty

EN

The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.

Słowa kluczowe

EN

partition; quasiorder; tolerance relation

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2016
• Tom: 45
• Numer: 2

Daty

wydano

2016-06-30

Twórcy

autor

Marek Nowak

• University of Łódź, Department of Logic

Bibliografia

• [1] I. Chajda, J. Niederle, B. Zelinka, On existence conditions for compatible tolerances, Czechoslovak Math. J. 26 (1976), pp. 304–311.
• [2] G. Czédli, Factor lattices by tolerances, Acta Scientiarum Mathematicarum 44 (1982), pp. 35–42.
• [3] S. N. Gerasin, V. V. Shlyakhov, S. V. Yakovlev, Set coverings and tolerance relations, Cybernetics and System Analysis 44 (2008), pp. 333–340.
• [4] A. I. Krivoruchko, Tolerance classes, Cybernetics and System Analysis 20 (1984), pp. 6–11.
• [5] M. Nowak, On some generalization of the concept of partition, Studia Logica 102 (2014), pp. 93–116.
• [6] J. Pogonowski, Tolerance spaces with application to linguistics, Adam Mickiewicz University Press, Poznań, 1981.
• [7] E. C. Zeeman, The Topology of the Brain and Visual Perception, [in:] M. K. Fort (ed.), The Topology of 3-Manifolds and Related Topics, 1962, pp. 240–256.
• [8] B. Zelinka, A remark on systems of maximal cliques of a graph, Czechoslovak Math. J. 27 (1977), pp. 617–618.

Identyfikatory

DOI

10.18778/0138-0680.45.2.01