퍼지 수 공간의 컴팩트 볼륵 집합에 관한 연구

On compact convex subsets of fuzzy number space

  • Kim, Yun-Kyong (Dept. of Information & Communication Engineering, Dongshin University)
  • 발행 : 2003.05.01

초록

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

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