A method for improving the consistency of fuzzy complementary judgement matrices based on satisfaction consistency and compatibility

Abstract

Focusing on the problem fuzzy analytic hierarchy process (FAHP), this paper investigates the inconsistency problems of preference information about alternatives expressed as a fuzzy complementary judgement matrix by a decision maker. Firstly, the average inconsistency index is selected to check whether the matrix meets the requirement of the consistency. Then, transform equation with a variable parameter is proposed after a fully consider of compatibility, and, a linear programming model is constructed under the constrain of both satisfaction consistency and compatibility to figure out the most suitable value of the variable parameter. Finally, the original matrix is transformed to an acceptable one, and the new method is illustrated with two numerical examples. © 2011 Springer-Verlag Berlin Heidelberg.