Transitive Coupling Problem

The Transitive Coupling Problem refers to the problem of interconnecting two multilevel subsystem models defined on the same contextual relation that is transitive.

Using the Implication Matrix Model

Warfield proposed the use of an Implication Matrix Model, which includes a reflexive binary matrix and an association (transitive relation). This concept adds really very useful information for ISM; however the practical use of this approach in some cases appears to be constrained by the size of the complete implication matrix and consequently the computer’s capabilities. If A matrix has dimensions m x m and B matrix has dimensions n x n, then the implication matrix would have 2(m x n) x 2(m x n). So as A and B increase in size, there will be difficulties in competing the implication matrix due to its large size.

Using square matrices of size equal to the total number of elements

Venkatesan proposed an alternate algorithm for transitive coupling which does not require the development of an implication matrix. Instead of the implication matrix, he suggested using only square matrices of size equal to the total number of elements involved in transitive coupling.

The two approaches achieve the same results. But Venkatesan’s approach appears to result in a higher number of questions than Warfield’s one. This happens possibly because of the different inference opportunity approaches for choosing an unknown.

Warfield recommends finding the current inference opportunity number of each unknown at any iteration using the implication matrix. Venkatesan, on the other hand, recommends finding the immediate inference opportunity number of each unknown at the beginning of the coupling process. Choosing an unknown for questioning using Venkatesan’s method may result in a different set of questions and possibly in a higher number of questions. However, it reduces the storage requirements.