An efficient procedure for transitive coupling in ISM

Transitive coupling is a procedure encountered in structuring complex systems using interpretive structural modeling (ISM). It involves the interconnection of two subsystems defined on the same contextual relation that is transitive. An efficient procedure or transitive coupling is proposed. The procedure presented is highlighted by savings in computer time and storage and by ease of programming. For a given value of one or zero for an unknown
x
_ij
or
y
_ij
, all inferences can be drawn with O(
mn
) computer time and θ((
m
+
n
)
²
) storage. Sufficient results obtained by a computer experiment using randomly generated problems are in close agreement with the results of the theoretical analysis.