A lot of literatures characterize an extension of an order on a set (say, X) to a weak order on the set of all of its non-empty subsets (say, F). This extension makes use of the information contained in the primitive order on X. This paper considers the case where the subsets of X are formed by a compatibility relation defined on X. As its main contribution, the paper attempts to show that an ordering can be defined on the collection of compatible subsets of a finite set endowed with a

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... lity relation. In particular, a necessary and sufficient condition is formulated that would guarantee when an ordering so defined turns out to be partial ordering.