View source for Transitive bordering

'''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. <br>

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 transitive coupling [4] is based.
* In [Societal Systems and Implication Structures for system interconnection matrices, Warfield has presented a technique that uses the [[Implication Matrix]].
* A procedure based on the following Theorem
To satisfy the constraints
A<sup>2</sup> + XY =  A
YX + B<sup>2</sup> = B

the following must hold for  all a k:
# if a<sub>lk</sub> = 0, then X<sub>lt</sub>Y<sub>tk</sub> = 0 for all t, and
# ifb<sub>lk</sub> = 0,then Y<sub>lt</sub>X<sub>tk</sub> = 0 for aall t.