This paper reviews and compares constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation. Different classes of rough set algebras are obtained from different types of binary relations. In the algebraic approach, one defines a pair of du...

A binary relation is (≤k)-reconstructible, if it is determined up to isomorphism by its restriction to subsets of at most k elements. In [8], Lopez has shown that finite binary relations are (≤6)reconstructible. To prove that the value 6 of its result, is optimal, Lopez [3], associates to all finite binary relation, an infinity of finite extensions, that are not (≤5)-reconstructible. These exte...

We consider expressions built up from binary relation names using the operators union, composition, and set difference. We show that it is undecidable to test whether a given such expression e is finitely satisfiable, i.e., whether there exist finite binary relations that can be substituted for the relation names so that e evaluates to a nonempty result. This result already holds in restriction...

In this paper S, X denote non empty sets and R denotes a binary relation on X . We introduce orthorelational structures which are extensions of relational structure and ComplStr and are systems 〈 a carrier, an internal relation, a complement operation 〉, where the carrier is a set, the internal relation is a binary relation on the carrier, and the complement operation is a unary operation on th...

Regularities in databases are directly useful for knowledge discovery and data summarization. As a mathematical background, relational algebra helped for discovering the main data structures and existing dependencies between the different attributes in a relational database. Functional, difunctional and other kinds of dependencies in a relational database describe invariant regular structures t...

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second bina...

A binary supermassive black hole leaves an imprint on a galactic nucleus in the form of a “mass deficit,” a decrease in the mass of the nucleus due to ejection of stars by the binary. The magnitude of the mass deficit is in principle related to the galaxy’s merger history, but the relation has never been quantified. Here, highaccuracy N-body simulations are used to calibrate this relation. Mass...