Results 301 to 310 of about 986,794 (335)

Representation of binary systems by families of binary relations

Israel Journal of Mathematics, 1969
It is proved that an arbitrary binary multiplicative system can be represented by a family of binary relations, using the so called generalized multiplication of relations. Transformations of such representations and existence of a ‘universal’ representation are studied.
D. Tamari, D. Tamari, A. Ginzburg, A. Ginzburg   +3 more
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Subgroups of Binary Relations [PDF]

, 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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The clone relation of a binary relation

Information Sciences, 2017
Abstract In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one.
Hassane Bouremel, Bernard De Baets, Lemnaouar Zedam, Raúl Pérez-Fernández   +3 more
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STRUCTURE OF FUZZY BINARY RELATIONS

Fuzzy Sets and Systems, 1981
The 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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Analysis of programs and binary relations

USSR Computational Mathematics and Mathematical Physics, 1983
Translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.2, 440-452 (Russian) (1983; Zbl 0523.68017).
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Binary relations as lattice isomorphisms

Annali di Matematica Pura ed Applicata, 1999
The main result of this paper shows that the semigroup \({\mathfrak B}_X\) of binary relations on a set \(X\) is isomorphic to a semigroup of triples of the form \((W,\varphi,V)\), where \(W\) and \(V\) are certain lattices and \(\varphi\colon W\to V\) is an isomorphism, with a multiplication which uses a ``sandwich matrix'' whose entries are again ...
Darel W. Hardy, Mario Petrich
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Transformation of binary relations

Proceedings of the Sixth International Conference on Computer Supported Cooperative Work in Design (IEEE Cat. No.01EX472), 2002
In the object-oriented paradigm, as complexity rises, the cost of developing and maintaining software systems grows exponentially. This complexity emerges from the continuous evolution of software systems to cope with changing requirements. This crucial problem can be dealt with by performing an active transformation of the elements (i.e.
E. Steegmans, J. Said
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Binary Relations and Permutation Groups

Mathematical Logic Quarterly, 1995
AbstractWe 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
Andréka, Hajnal, Düntsch, Ivo, Németi, István   +2 more
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The lattice of idempotent binary relations [PDF]

Algebra Universalis, 1979
Order-theoretic properties of the complete latticeE(A) of indempotent binary relations ρ=ρ2 on the given setA are investigated. The elements ρ ofE(A) are classified according to theirfixed field I(ρ)={a∈A|(a, a)∈ρ} as being either offinite type, dense, or ofmixed type.
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Complete Semigroups of Binary Relations

Journal of Mathematical Sciences, 2003
This paper considers the subgroups of the semigroup of binary relations \(B_X\) consisting of binary relations \(R\) whose sections \(S_x=\{y\mid(x,y)\in R\}\) are always members of a complete semilattice \(D\) of subsets of \(X\) under union. These semigroups can also be studied in terms of Boolean matrices and have applications to graph theory ...
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