Appendix A

The ‘CWV determination’ phase involves obtaining the criteria weights for the constructs and factors, i.e., the ‘CWV for the constructs’ representing the relative importance of the constructs w.r.t the (total) decision goal and a ‘CWV for factors’ representing the relative importance of the factors w.r.t each construct. The absolute importance of all factors can be obtained by multiplying each element in the CWV for the constructs (scalarly) with the corresponding CWV for the factors under each construct.

The ‘alternative selection’ phase involves evaluating the weights for each alternative in terms of all criteria. This is done by obtaining a CWV carrying the relative importance of all alternatives w.r.t each factor (i.e. the ‘CWV for alternatives’; we use the term ‘CWV’ rather than ‘priority’ for naming consistency). Then, using the simple-additive weighting (SAW) method (also called the weighted sum model (WSM) method), the absolute importance of factors obtained in the former phase are further imposed on each ‘CWV for alternatives’, and thus the ‘score’ for each alternative can be aggregated. These scores form a ‘score vector’ (SV), which is the basis for ranking the alternatives and obtaining the final rank order vector (ROV).

Consistency check is another substantial element of AHP, in order to verify all of the above result CWVs. It is, in fact, a robustness test for the PCMs answered by the respondent. This relies on the computation of the consistency ratio (CR), which is the quotient of the dividend CI (consistency index) and the divisor RI (random index), where CI is calculated on the basis of the PCM information using the eigenvalue concept in linear algebra, and the value of RI can be obtained from a fixed table (as with many other statistical methods) (Saaty, 2003). We refer to a systematic vector-based digest of the above calculation processes in further detail (Zhuang et al., 2019).

Appendix B

This section lists the numerical result tables for the correlation coefficients (Table A1) and the cosine similarity indices (Table A2) computed in a pair-wise manner on the basis of the individual opinions of the same set of 36 respondents whose opinions passed the CR-validation at the constructs level (with respect to the decision goal).

 

 

 

Table A1

    a

 

    b

 

    c

 

    d

 

 

 

Table A2

    a

 

    b

 

    c

 

    d