There is no mathematical validity for using fuzzy number crunching in the Analytic Hierarchy Process

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Dec, 2006

Journal: Journal of Systems Science and Systems Engineering
Vol.: 15- Issue: 4- Pages: 457-464

Abstract: Fuzzy logic has difficulty producing valid answers in decision-making. Absent are theorems to prove that it works to produce results already known that are being estimated with judgments by transforming such judgments numerically. The numerical representation of judgments in the AHP is already fuzzy. Making fuzzy judgments more fuzzy does not lead to a better more valid outcome and it often leads to a worse one. The compatibility index of the AHP is used to illustrate how the answers obtained by fuzzifying AHP judgments do not produce better results than direct derivation of the principal eigenvector. Other authors who did experiments with given data in decision making quoted in the conclusions section of the paper, have observed that fuzzy sets gives the poorest answers among all methods used to derive best decisions.

Keywords: AHP, Analytic Hierarchy Process, Fuzzy, Compatibility, Validation