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Binary Relations and Permutation Groups
Mathematical Logic Quarterly, 1995AbstractWe discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed
Hajnal Andréka +2 more
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Set operations over compressed binary relations [PDF]
Information Systems, 2019 [Abstract]: Binary relations are commonly used to represent relationships between real-world objects. Classical representations for binary relations can be very space-consuming when the set of elements is large. In these cases, compressed representations,
Miguel Herbon Penabad +2 more
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Normal forms for binary relations
Theoretical Computer Science, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Claudio Gutiérrez +1 more
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On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2019Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation.
Omar Barkat +2 more
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Hyperstructures associated with binary relations
Computers and Mathematics With Applications, 2006 Given a binary relation \(R\) on a non-empty set \(H\), a hyperoperation \(\odot_R\) is defined on \(H \times H\) by \(x \odot_R y = \{z \in H \mid xRz, zRy\}\). \((H,\odot_R) \) is a hypergroupoid \(\Leftrightarrow R \circ R = H \times H\) [\textit{P. Corsini}, ``Binary relations and hypergroupoids'', Ital. J. Pure Appl. Math.
Spartalis Spartalis, C. Mamaloukas
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1974
A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations.
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A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations.
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On a binary relation inference network
[1991] Proceedings. The Fifth International Parallel Processing Symposium, 2002Many human and machine reasoning tasks require complicated inferences between objects and events, in which the constituting inference processes depend in turn on successive inferences on more basic binary relations. Given a set of n binary relations between m different objects or events, it is possible to infer other consistent binary relations, to ...
Kai-Pui Lam, Crystal J. Su
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An algebraic approach to binary relations
Asian-European Journal of Mathematics, 2015Several attempts were made to assign to a given binary relation a certain binary operation in order to allow an algebraic approach for investigating binary relations. However, the previous attempts by the first two authors were restricted to the case of so-called directed binary relations.
Chajda, Ivan +2 more
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STRUCTURE OF FUZZY BINARY RELATIONS
Fuzzy Sets and Systems, 1981The structure of fuzzy binary relations of indifference and preference is studied. The full description of fuzzy equivalence relations in terms of fuzzy partitions is given. All possible logical relations between various transitivity properties of fuzzy preferences are established.
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On binary operators and their derived relations
BIT, 1988Considering a list of abstract binary operations and relations, the author gives a sequence of seven simple to prove, but interesting and very useful theorems, which appear frequently in algebra and other fields. All results are known, but the approach is nice and appropriate for teaching, with a good generality.
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