"A Minimization Approach to Membership Evaluation in Fuzzy Sets and Error Analysis"

Journal of Optimization Theory and Applications, 1990, Vol. 66, No. 2, pp. 275-287.

E. Triantaphyllou, P.M. Pardalos, and S.H. Mann

Evaluation of the degree of membership in fuzzy sets is a fundamental topic in fuzzy set theory. Saaty (Ref. 1) proposes a method for solving this problem that has been widely accepted. In this paper we examine the problem from an error minimization point of view that attempts to reflect the real intentions of the decision maker. When this approach is used, the findings reveal that fuzzy sets of different cardinalities have dramatically different requirements in the consistency level of the input data as far as the error minimization criterion is concerned.

Key Words:
Fuzzy set, degree of membership, eigenvector, least squares problem, decision making.

Download this paper as a PS (PostScript) file (size = 866 KB).

Download this paper as a PDF file (size = 866 MB).

Visit Dr. Triantaphyllou's homepage.