Fuzzy Judgments and Fuzzy Sets

Fuzzy Judgments and Fuzzy Sets

Thomas L. Saaty (University of Pittsburgh, USA) and Liem T. Tran (University of Tennessee, USA)
Copyright: © 2012 |Pages: 17
DOI: 10.4018/978-1-4666-1589-2.ch006
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Abstract

Using fuzzy set theory has become attractive to many people. However, the many references cited here and in other works, little thought is given to why numbers should be made fuzzy before plunging into the necessary simulations to crank out numbers without giving reason or proof that it works to one’s advantage. In fact it does not often do that, certainly not in decision making. Regrettably, many published papers that use fuzzy set theory presumably to get better answers were not judged thoroughly by reviewers knowledgeable in both fuzzy theory and decision making. Buede and Maxwell (1995), who had done experiments on different ways of making decisions, found that fuzzy does the poorest job of obtaining the right decision as compared with other ways. “These experiments demonstrated that the MAVT (Multiattribute Value Theory) and AHP (Analytic Hierarchy Process) techniques, when provided with the same decision outcome data, very often identify the same alternatives as ‘best’. The other techniques are noticeably less consistent with the Fuzzy algorithm being the least consistent.”
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2. Fuzzy, Ahp, Eigenvalue And Eigenvector

Fuzzy set theory uses the AHP to drive fuzzy priorities that are already obtained by calculating the eigenvector. It relies on using the eigenvalue to improve inconsistence although it is known that a perfectly consistent matrix does not of necessity yield a valid result in that it is a best estimate of underlying measurements when such measurements are known. It is largely the quality of the judgments that determines the validity of the outcome ands not their numerical precision. When the matrix is inconsistent we need the eigenvaector to derive priorities.

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