A set of zero-one matrices satisfying (CC1)–(CC4) is called a coherent configuration. It is really a combinatorial object, since the conditions on the matrices can be translated into combinatorial conditions on the binary relations Oi. The coherent configuration formed by the orbital matrices of a permutation group G is the orbital configuration of G. Indeed, a coherent configuration is a parti...

An ordered monoid is a structure with an identity element (1′), a binary composition operator (;) and an antisymmetric partial order (≤), satisfying certain axioms. A representation of an ordered monoid is a 1-1 map which maps elements of an ordered monoid to binary relations in such a way that 1′ is mapped to the identity relation, ; corresponds to composition of binary relations and ≤ corresp...

the complexation reactions between mg2+, ca2+, sr2+ and ba2+ metal cations with 15-crown-5 (15c5) were studied in acetonitrile (an)-methanol (meoh) binary mixtures at different temperatures using conductometric method. 15c54 forms 1:1 complexes with mg2+, ca2+ and sr2+ cations in solutions. the ma2+ cation forms a 2:1 complex (ratio of lighand to cation) in solutions. a linear relation was obse...

The rough set theory usually is used in datamining. At this time, we will suppose the approximation operator to satisfy some wonderful properties. It need us to think about the basis algebra, the binary relation and the approximation operator’s form in the rough set model. Lfuzzy rough approximation operator is a general fuzzy rough approximation operator. Comparing with the others rough approx...