An evaluation of the eigenvalue approach for determining the membership values in fuzzy sets

Abstract The membership values of the elements of a fuzzy set of key importance in any theoretical or practical application of fuzzy set theory. Although there are many methods that evaluate membership values, the methd proposed by Saaty [8,9] based on matrix of pairwise comparisons and eigenvalue theory, is the backbone of many other methods. In this paper we evaluate the above method by using a forward error analysis approach with the assumption that the true membership values in a fuzzy set are continuous in the interval (0, 1). The results reveal that the eigenvalue method is dramatically inaccurate even for fuzzy sets with few members.