The fuzzy set membership problem using the hierarchy decision method

Abstract

Abstract The membership values of the elements of a fuzzy set are central to any discussion of fuzzy set theory. This paper investigates the soundness of using the Analytic Hierarchy Decision Model of T.L. Saaty for the purpose of specifying the fuzzy set membership values. Other papers have posed the question and have shown experimentally through other methods that no specific evaluation technique within the framework of the model always obtains the best calculable membership values. This work defines a different metric to measure a best calculable membership vector and argues that the input data is sufficiently restrictive that the numerical precision being sought simply cannot be obtained. Thus the Analytic Hierarchy Decision process remains a valuable first stage heuristic, but it can not be expected to report fine grain differences in membership values.