Consistency and ranking method for I type uncertain number complementary judgment matrix

This paper deals with the decision problem where the preference information is given as the I type uncertain number (interval number, triangular fuzzy number or trapezoidal fuzzy number) complementary judgment matrix. Firstly, we introduce the definitions of I type uncertain number complementary judgment matrixes. Then we discuss the consistency aspect including the consistency definition and method to construct a consistent I type uncertain number complementary judgment matrix. For further discussion of consistency and deriving priorities of alternatives, we propose the definition of expected value matrix. Based on expected value matrix, we derive the priorities of alternatives when the judgment information is I type uncertain number complementary judgment matrix. Finally, two illustrative examples are also given.