For developing the intuitionistic fuzzy aggregation operators to handle intuitionistic fuzzy multi-criteria fuzzy decision making problems, the most important issue is how to find an addition-invariant partial order to construct an ordered addition monoid of intuitionistic fuzzy values. In this paper, we point out that Atanassov's order is not a totally partial order, and the popular partial order, Xu's modified lexicographic partial order, is not addition-invariant, both of them can not be used for constructing an ordered monoid of intuitionistic fuzzy values, furthermore, a simple partial order based on natural lexicographic order is proposed, the author prove that this order is a totally partial order and addition-invariant, which can be used for constructing an ordered addition monoid of intuitionistic fuzzy values
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