"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.

Key Words:
Fuzzy set; degree of membership; eigenvector; pairwise comparisons; decision making.

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