The Study On The Consistency Of Fuzzy Complementary Judgment Matrix

Fuzzy Analytic Hierarchy Process (FAHP) is a method containing fuzzy thoughts based on AHP and has become more and more important in society, economic, management fields in recent years. Meanwhile, the fuzzy complementary judgment matrix used in FAHP has been a vital research topic. So this thesis did research on the consistency of such matrix.For the complementary judgment matrix with real numbers, the thesis discussed the relationship between the elements and the weights. To additive consistency, the existing conclusions were compared and to the multiplicative consistency, a strict proof was given to an existing theorem.For the complementary judgment matrix with fuzzy numbers, the interval number, triangle number, and trapezoid number, the thesis mainly discussed the relationship between the elements and the weights under the consistency. Then the thesis gave the definitions of the 2nd additive consistency and the division consistency.Since the conditions of the consistency are too strict and seldom met in the reality, so various consistency are studied in the following chapter, including strong additive (multiplicative) consistency, weak additive (multiplicative) consistency, tolerant additive consistency, approximate additive consistency, square multiplicative consistency and so on. What's more, the properties and the relationship are considered for the above consistency.The last chapter studied the definition and core consistency, expected consistency of mixed complementary and then discussed the definitions of the consistency of the reciprocal and complementary judgment matrix. Meanwhile, the conversion between the reciprocal matrix and the complementary matrix were studied, two theorems were brought out.