A completed partial order of ordered semi-vector space of intuitionistic fuzzy values

Abstract

For developing the intuitionistic fuzzy aggregation operators to handle intuitionistic fuzzy multicriteria fuzzy decision making problems, two popular partial orders are used, one is Atanassov's order and the other is Xu's Both of them disregard the following important condition, feasible partial order must be not only a totally partial order but also an operation-invariant partial order. In author's previous work, it is pointed out that the former is not a totally partial order, and the latter is not addition-invariant, both of them are not feasible enough to construct the intuitionistic fuzzy aggregation operators. In this paper, the author further point out that Xu's order is not only not addition-invariant but also not scalar multiplication-invariant, and further prove that author's partial order is not only a totally partial order and addition-invariant, but also scalar multiplication-invariant, which can be used for constructing an ordered semi-vector space of intuitionistic fuzzy values to handle intuitionistic fuzzy multi-criteria fuzzy decision making problems.