On Approximation of Fuzzy Sets by Crisp Sets: From Continuous Control-Oriented Defuzzification to Discrete Decision Making

Authors

Hung T. Nguyen
Witold Pedrycz
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

9-2000

Comments

UTEP-CS-00-30.

Published in Proc. of International Conference on Intelligent Technologies, Bangkok, Thailand, December 13-15, 2000, pp. 254-260.

Abstract

In this paper, we show that the necessity to make crisp decisions in uncertain (fuzzy) situations leads to the necessity to "approximate" fuzzy sets by crisp sets. We show that seemingly natural approximation ideas - such as using alpha-cut for a given alpha - often do not work, and we describe new approximations which not only work, but which are optimal in some reasonable sense