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DYNAMIC AVERAGING PROCESS FOR INCOMPLETE INFORMATION CASE

Dynamic Averaging Process is studied for the incomplete information case where some elements in a pairwise comparison matrix are missing. As the averaging operation of a DAP, the generalized mean with the p-th power, or the p-th power mean, is considered. Note that those with p=1,p=-1, p→0, and p→+∞ are the arithmetic mean, the harmonic mean, the geometric mean and the maximum operation, respectively. First, we prove that the convergent weight vector of a geometric DAP, or the DAP with geometric mean averaging (the power mean with p→0), is equal to the LLS(Logarithmic Least Square) solution under the reciprocity condition ( × ), the self-identity condition( ),etc. Second, the Harker method is modified in two ways so that it can cope with the p-th power mean and it can take into account the effect of the eigenvector λ, or the stationary state rate. Third, we prove that the convergent weight vector of a p-th power DAP, or a DAP with the p- th power averaging(power mean with p≠0), is equal to the convergent weight vector of the modified Harker method under the stationarity condition (x(t)=λx(t-1), or the existence of the stationary rate λ). Finally, since a DAP can be regarded as the power method for calculating an eigenvector for the generalized algebraic system, the possibility of using the geometric DAP, or the LLS, is discussed to estimate the weight vector for the incomplete information case.