The paper is devoted to a concept of aggregation of binary fuzzy relations. Consider two n-ary vectors, when we know the degrees to which corresponding components are in relation we can measure the degree to which vectors are in relation. Tasks with such background justify the necessity of aggregation of binary fuzzy relations and we contribute to the topic in this paper. First we recall the ap...

In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the ba...

Social choice theory concerns itself with the proper choice of a social state from a given feasible set of social states. The main question the theory addresses is how that social choice should depend on the profile of individual preferences. Early work by Arrow and various predecessors, including Condorcet, Borda, Dodgson and Black, was about the construction of a social preference ordering — ...

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary relations. We consider Kleene allegories, i.e., Kleene algebras with two additional operations and a constant which are natural in binary relation models: inter...

Experimental data on angular distributions of γ rays emitted from binary and ternary spontaneous fission of 252 Cf are analyzed. Their difference indicates that the alignment of fragments is higher in ternary fission than in binary one. The consequences of possible relation between the mechanism of ternary fission and the excitation of collective modes during the saddle-to-scission stage are di...

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary relations. We consider Kleene allegories, i.e., Kleene algebras with two additional operations and a constant which are natural in binary relation models: inter...

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

In this paper X denotes a set, R, R1, R2 denote binary relations, x, y, z denote sets, and n, m, k denote natural numbers. Let us consider a binary relation R on X. Now we state the propositions: (1) fieldR ⊆ X. (2) If x, y ∈ R, then x, y ∈ X. Now we state the propositions: (3) Let us consider sets X, Y . Then (idX)Y = X ∩ Y . (4) 〈x, y〉 ∈ R |2 X if and only if x, y ∈ X and 〈x, y〉 ∈ R. (5) dom(...

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.