Pseudodimension of relational structures

Transitivity properties of ternary fuzzy relations

“…We denote by T t the transpose of T , i.e., for any x, y, z ∈ X, T t (x, y, z) = T (z, y, x). For more details on (fuzzy) ternary relations, we refer to [1,7,19,22,29].…”

“…In recent years, the interest in ternary relations is on the rise, as they play an important role in many theoretical and applied areas. From a theoretical point of view, ternary relations have been studied in mathematics (e.g., in algebra [7,19], in (fuzzy) triadic formal concept analysis [5,14,18] and in logic [21]). In applications, (fuzzy) ternary relations can be found in many different areas, for instance in social sciences (e.g., philosophy [3]), in biology (e.g., modelling of phylogenies [28]), in computer science (e.g., the Resource Description Framework (RDF) [27]).…”

On a product of universal hyperalgebras

“…Several authors then extended the cardinal arithmetic to relational systems -see e.g. [6][7] and [9][10]. Conversely, the cardinal arithmetic has been restricted from relational systems to universal algebras in [11], to partial algebras in [14] and to hyperalgebras in [13].…”

ON EXPONENTIATION AND MULTIPLICATION OF n-ARY HYPERALGEBRAS

“…Birkhoff's direct arithmetic of partially ordered sets [1] was extended to relational systems by several authors, see, e.g., [6,7] and [9,10]. Conversely, the cardinal arithmetic has been restricted from relational systems to (n-ary) algebras in [11], to partial algebras in [13] and to hyperalgebras in [12].…”