On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States
Liem Tran
Department of Geography
University of Tennessee
United States

Publication date: Oct, 2007

Journal: Mathematical and Computer Modelling
Vol.: 46- Issue: 7-8- Pages: 962-975

Abstract: Fuzzy set theory has serious difficulties in producing valid answers in decision-making by fuzzifying judgments. No theorems are available about its workability when it is applied indiscriminately as a number crunching approach to numerical measurements that represent judgments. When judgments are allowed to vary in choice over the values of a fundamental scale, as in the Analytic Hierarchy Process, these judgments are themselves already fuzzy. To make them fuzzier can make the validity of the outcome, when the actual outcome is known, worse, as shown by several examples in this paper. Also, improving the consistency of a judgment matrix does not necessarily improve the validity of the outcome. Validity is the goal in decision-making, not consistency, which can be successively improved by manipulating the judgments as the answer gets farther and farther from reality. An example of this is included.

Keywords: Fuzzy sets, Analytic Hierarchy Process, AHP