A New Grey Relational Analysis Function Based on Harmonic Mean

Abstract

This study proposes a new harmonic mean (HM) GRA function based upon the harmonic mean of all attributes, and is used to enhance the applications of GRA. This study also categories all of the existing GRG models into different types basically according to the kernel function Each type has the special characteristics and limitations and is complemented to each other in the GRG ranking using GRA function. Grey relational analysis (GRA) functions provide an effective means of solving multiple-criteria decision problems by ranking the potential solutions in terms of their so-called Grey relational grades (GRGs) such that the optimal solution can be easily determined. The proposed GRA function, in which the Attribute Impulse Factors and a different formula of GRG were defined, belongs to the HM type, and could be calculated indirectly from the harmonic mean of all attributes. In mathematics, the harmonic mean is one of several kinds of average. Some illustrations were used to compare the GRG results obtained using the proposed GRA function of HM type with those of GRA functions of other types. Finally, some useful conclusions deducted from discussions.