Additive consistency of complementary judgment matrices with fuzzy numbers

The consistency of complementary judgment matrices with fuzzy numbers is studied. Definitions of triangular fuzzy number complementary judgment matrix, trapezoidal fuzzy number complementary judgment matrix as well as hybrid number complementary judgment matrix are given, followed by definitions of core operator and core matrix. Meanwhile, definition of consistency of fuzzy number complementary judgment matrix is given based on core matrix. Method for identifying the degree of additive consistency is given by establishing the reachable matrix. By constructing and analyzing the deviation matrix, approaches to improving the additive consistency of inconsistent triangular fuzzy number complementary judgment matrix, inconsistent trapezoidal fuzzy number complementary judgment matrix and inconsistent hybrid number complementary judgment matrix are proposed. For an inconsistent judgment matrix with fuzzy numbers, the rectifying value can be a fuzzy number or an exact one. A numerical example is given to illustrate the method's practicability. The method proposed provides a feasible approach to judge and improve the consistency of complementary judgment matrix with fuzzy numbers.