"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.
Fuzzy set, degree of membership, eigenvector, least squares
problem, decision making.