## 1 Introduction
[4] used a hybrid MADM approach, AHP-GTMA (analytic hierarchy process and a graph theory and matrix approach), to model such a selection decision problem. For how the AHP-GTMA model was formulated in [4], see the digested review in Appendix A for details. In summary, the main contributions of [3; 4] are the novelty to scientifically manage/support the encountered selection decision for the first time, to identify a suitable criteria set for the problem and to solve the problem systematically using the hybrid AHP-GTMA model. These are important for making a purchase decision and for addressing the design issues of paper shredder. However, apart from these, there is a question as to _whether one such relatively recent approach is effective to aid a selection decision problem (such as the abovementioned) in industrial practice._  
In terms of operational research (OR) applications, using only one single method to solve a certain type of problem is not always plausible. Thus, often, whether another method can be used to solve the same problem, the results of that process and the possible comparisons made (between the method used before and the one used after) are of interest. That is to say, using an arbitrary approach to have a solution could be deemed appropriate, as long as there is problem-model fitness and it is the first time to scientifically manage the encountered decision. This is exactly the contributions of [4]. However, this also implies that _the effectiveness of using the AHP-GTMA method has not yet been cross-validated or at least verified._  
Therefore, this paper proposes a rank-based, multi-measure comparative research flow to benchmark the effectiveness of AHP-GTMA on solving the target selection decision problem. The original paper selection problem is used as the exemplar problem that is to be solved separately by using AHP-GTMA and another rival approach. The rival approach must be a \"credible\" one to ground the claims made based on the results from the comparisons. In the experiment that applied the proposed flow, the well-known AHP-TOPSIS method, which has been applied to various fields, is introduced as the rival approach not only because of its credibility but also for the sake of its model-problem fitness. The entire flow compares the results and validates the similarity in the results that are separately solved using the two models. For the two models used in this study in particular, subject to the validated similarity, the effectiveness of the AHP-GTMA model can be underlain by reference to the results from using the widely-applied AHP-TOPSIS method. In other words, the effectiveness of AHP-GTMA in solving a selection problem in practice is therefore verified by the verified similarity between the results. The proposed flow is rank-based because it takes only the rank order vectors (ROVs) (i.e., the output of most of the MADM models, to the authors' knowledge [5]) that are solved individually by two MADM models as the required information for input. (A final ordinal rank is usually determined by the ROV, wherein each element indicates the preferential order of an alternative. Usually, this vector is determined by, and is the result of, prioritizing another \"score vector\" that carries information about the \"assessed scores\" for all of the alternatives in the given selection problem. See [PERSON] and [PERSON]'s book [5] for more detail, which was re-printed in 2011 [6]. In addition, the mentioned term \"score\" has different forms when different MADM methods are used. For example, using TOPSIS, the relative closeness index (RCI) connotes the \"score\" for an alternative. For another example, using GTMA, the permanent value of an ASAM matrix connotes the \"score\" for an alternative. These are the basis to prioritize the alternatives, to name but a few.) It is a multi-measure flow because different concepts are used to solidify and cross-validate the results from comparison: the arithmetic based, the geometrical (vector distance) based and even the statistical (non-parametric) based ones.