Complemented tolerances on lattices (original) (raw)
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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz Časopis pro pěstování matematiky, rol, 102 (1977), Praha
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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz Časopis pro pěstování matematiky, roř. 101 (1976), Praha
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2021
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventieth of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([6]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radelecki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. AMS Subject Classification: 08A02, 08A05, 06A06, 06A11
On the tolerance extension property
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Notes on locally internal uninorm on bounded lattices
Kybernetika (Praha), 2017
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Approximation lattices defined by tolerances induced by irredundant coverings
Miskolc Mathematical Notes, 2019
The topic of rough set theory considers a relation to determine the lower and upper approximations of a set X. Originally, this relation was assumed to be an equivalence relation. This research focuses on using tolerance relations instead of equivalences, i.e. we do not assume the transitivity of the relations. More specifically, in this paper we investigate tolerances induced by irredundant coverings. We characterize the interrelation between the lattices of lower and upper approximations of such tolerances R and. The theory of Formal Concept Analysis makes it possible to examine the inclusions of the resulting concepts. We also use quasiorders (denoted by E. / and D. /) and an equivalence relation (denoted by ker) for summarizing the connection between tolerances and lattices in a theorem.