An addition-invariant partial order of ordered addition monoids of intuitionistic fuzzy values

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 additioninvariant, which can be used for constructing an ordered addition monoid of intuitionistic fuzzy values.