A procedure of implication using quantifiable binary relations for structural modeling

In the field of system engineering, numerous proposals have been made for structural modeling. In the many structural modeling methods, the first process is to make a binary relation matrix. This process is difficult because the number of questions to extract binary relation is ; where n is the number of elements. Structural modeling can be divided into two types. One has a 0-1 type of binary relation. Another has a quantifiable, more general, binary relation. In the former, this process supposes the relation has a transitive property, it infers the unknown binary relation using the transitive property. But the latter has no such procedure in this process. So the authors propose a procedure in this paper. The proposed procedure is based on the same idea as the former. Suppose the binary relation has the transitive property; it infers the unknown binary relation using this. In this paper, the quantifiable binary relation is represented by a rank scale. The set of system elements is (n is the number of system elements). ( has R relation to shown ). Finite ordinal set means quantifiable binary relation for all . The binary relation must have ‘reflexive property’ and ‘transitive property’ like reflexiveness and transitiveness. The reflexive property is . The transitive property is . [In Japanese.]