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Networks are served to be tangible and appropriate tools for decision-making on complex and diverse issues where analysis by other means will occasionally demand lenghty calculations. There are different options to find the shortest track in a network. The intended options have been designed on the basis of a single or
several criteria such as distance, cost, time, and where sums of
each criteria will characterize additivity. Now if a decision-maker intends to simultaneously use several different, and often opposite criteria, with some of them lacking in additvity, to move from the
origin to a destination, which will be the best track? This article attempts to present a model of the best track in such networks.