Extremal problems of approximation theory in fuzzy context
The problem of approximation of a fuzzy subset of a normed space is considered. We study the error of approximation, which in this case is characterized by an L-fuzzy number. In order to do this we define the supremum of an L-fuzzy set of real numbers as well as the supremum and the infimum of a crisp set of L-fuzzy numbers. The introduced concepts allow us to investigate the best approximation and the optimal linear approximation. In particular, we consider approximation of a fuzzy subset in the space L-p(m) of differentiable functions in the L-q-metric. We grove the fuzzy counterparts of duality theorems, which in crisp case allows effectively to solve extremal problems of the classical approximation theory. (C) 1999 Elsevier Science B.V. All rights reserved.
extremal problem error of approximation best approximation l-fuzzy real number supremum of an l-fuzzy subset of real numbers approximation of an l-fuzzy set width of an l-fuzzy set