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There is no mathematical validity for using fuzzy number crunching in the analytic hierarchy process

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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.

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References

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  1. University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Thomas L. Saaty

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  1. Thomas L. Saaty
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Correspondence to Thomas L. Saaty.

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Thomas L. Saaty is a member to the U.S. National Academy of Engineering, holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that, he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics…all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and government.

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Saaty, T.L. There is no mathematical validity for using fuzzy number crunching in the analytic hierarchy process. J. Syst. Sci. Syst. Eng. 15, 457–464 (2006). https://doi.org/10.1007/s11518-006-5021-7

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  • DOI: https://doi.org/10.1007/s11518-006-5021-7

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