"An Evaluation of the Eigenvalue Approach for Determining the
Membership Values in Fuzzy Sets"
Fuzzy Sets and Systems,
1990, No. 35. No. 3, pp. 295-301.
E. Triantaphyllou and S.H. Mann
The membership values of the elements of a fuzzy set are a key
importance in any theoretical or practical application of fuzzy set
theory. Although there are many methods that
evaluate membership values, the method proposed by Saaty [8, 9]
based on a 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.