## 3 Decision Case Modeling and the Comparisons: Methods and the Results  
### Comparative Research Flow  
Most MADM studies suppose that there are \(m\) alternatives and \(n\) criteria (attributes) for a given decision system of a selection decision problem, \(P\). An \(m\)\(\times\)\(n\) \"decision matrix\", \(D\), wherein each element contains a value of an alternative that is evaluated based on some considered attribute, is established by data collection. The data collection process could involve many heterogeneous data sources, such as human data, computer data, network data, archived database data, paper profile data or electronic data, etc., subject to the recent trend of data-driven decision-making (DDDM). Usually, before the model calculations begin, the initial decision matrix (\(D\)) is normalized to give another \"normalized decision matrix\", which is \(D^{\prime}\). In addition, the opinion of a DM about the pairwise relationship between any two given attributes can be polled using an AHP-style expert questionnaire. A pairwise comparison matrix, \(B\), is then obtained and this serves as the basis to determine a priority vector, which is the \(CWV\) over the considered attributes. Using the data specifications as defined (and required) by AHP-GTMA and by AHP-TOPSIS, \(D^{\prime}\) and \(B\) are the sufficient input information for AHP-GTMA modeling, whilst \(D^{\prime}\) and \(CWV\) are sufficient for AHP-TOPSIS modeling. By using \(E=\{D^{\prime},B\}\) as the data catalogue and solving \(P\) using AHP-GTMA, the ROV, \(ROV_{\text{AHP-GTMA}}\), whose elements contain the rank orders that are determined for the alternatives, is obtained as the final output of this AHP-GTMA modeling. Similarly, by using \(F=\{D^{\prime},\)\(CWV\}\) as the data catalogue for \(P\) and solving it again using AHP-TOPSIS, another ROV, \(ROV_{\text{AHP-TOPSIS}}\), is then obtained as the final output of this AHP-TOPSIS modeling. In this study, the first and core logic of the proposed comparative research flow is that, for \(P\), whether \(ROV_{\text{AHP-GTMA}}\) and \(ROV_{\text{AHP-TOPSIS}}\) are similar is important. That is, if \(ROV_{\text{AHP-GTMA}}\) \"can be\" similar to \(ROV_{\text{AHP-TOPSIS}}\) upon modeling the same known decision problem in practice, the effectiveness of AHP-GTMA (which is relatively new and with fewer existing applications) is therefore verified because the rival AHP-TOPSIS approach is a \"widely used\" and experienced method. The second logic pertains to \"how to determine\", instead of to \"whether there is\", the similarity between the individual results obtained from two models. This involves two questions for the methodology of comparison: (1) The degree to which they are similar must be measured in a numerical sense, but how? (2) In the \"individual results\", what type of message should be taken for the similarity measurement? The latter question can be examined earlier for illustration clarity. To keep convenience of use when the proposed flow is applied, this study advocates that only the information about ordinal rank, which is the final output of almost every MADM model, is the input of the flow. That is, comparisons should be made and the similarity should be identified solely based on the two ROVs, rather than introducing any other type of result information which is perhaps in common. This is the reason the proposed comparative research flow is \"rank-based\". The answer to the former question relates to the above answer to the latter question, because the possible way(s) to measure the similarity numerically depends on what is to be measured. In our study, since the similarity between the individually-obtained ROVs are of interest and it contains the numerical values of ordinal rank, each of which is assessed for an alternative, several tangible/intangible measures can be established in terms of different theoretical aspects, as follows:  
1.