Abstract:

A method minimizing ranking vectors’ distances is proposed for a decisionmaking problem with ranking vectors of the alternatives given by decision makers in respect to each attribute considered. A distance function for ranking vectors is developed and proved to satisfy the conditions proposed by Cook and Seiford. Then a nonlinear integer programming model minimizing decision makerweighted distance between the rankings of the alternatives for the group and the ones for every decision maker is developed and solved by an exhaust algorithm to obtain the rankings of the alternatives for the group in respect to each attribute. With attributeweighted distance between the integrated rankings of the alternatives and the ones under every attribute being minimized, similarly, the final rankings of the alternatives for the group are determined. A supplier selection case is presented to illustrate the proposed method, and some discussions on the results verifies its effectiveness. This work extends Cook-Seiford social selection function to multi-attribute group decisionmaking, and can obtain a unique ranking result for a problem.