Comparison of asymmetric and symmetric decision-making bases in generalised grey target decision method for mixed attributes

Purpose The decision-making basis (DMB) of generalised grey target decision method (GGTDM) for mixed attributes could be divided into asymmetric and symmetric ones. The asymmetric DMB differs from the distance measure that has the characteristic of symmetry in common sense. This may affect the decision-making result and impede the application of GGTDM sometimes. To address this issue, the asymmetric DMB of GGTDM for mixed attributes could be extended to a symmetric one, which is investigated. Design/methodology/approach The theoretical framework of asymmetric DMB of GGTDM for mixed attributes that could be extended to a symmetric one is first built. Then the asymmetric DMBs for which the proximity and Kullback–Leibler (K-L) distance could be extended to symmetric ones are researched. Next, the advantages and disadvantages of the asymmetric and symmetric DMBs of GGTDM for mixed attributes are investigated. Finally, the application and comparison analysis verify the proposed approaches. Findings The comparison of asymmetric DMBs and symmetric DMBs shows that: given the same mixed-attribute-based alternatives, the asymmetric proximity is preferred if adopting proximity as the DMB; however, the symmetric K-L distance is better than that of the asymmetric one if K-L distance-based DMB is selected. Originality/value This work extends the asymmetric DMB of GGTDM to a symmetric one and discusses how to employ them (asymmetric and symmetric DMBs) considering the simple calculation process and the accuracy of decision-making results.