Transitive Bordering is a special case of transitive coupling in which the subsystem B consists of a single element.
Transitive Bordering is used for adding a new element to an already existing binary matrix model.
Transitive Bordering can also be employed iteratively in the ISM process for developing the complete binary matrix as soon a portion of the matrix, representing a subset of the set of elements, is filled.
Techniques
- A method that requires the derivation and solution of a set of characteristic logic equations. Warfield [5, Ch. 7]. This approach uses the same principle on which the cascading technique for transi- tive coupling [4] is based.
- In [1] and [2], Warfield has presented a second technique involving the implication matrix.
- A procedure based on the following Theorem
To satisfy the constraints A2 + XY = A YX + B2 = B
the following must hold for all a k:
- if alk = 0, then XltYtk = 0 for all t, and
- ifblk = 0,then YltXtk = 0 for aall t.