This paper discusses various techniques for soft decision making by neural
networks. Decision making problems are described as choosing an action from
possible alternatives using available information. In the context of soft
decision making, a single action is not always chosen. When it is difficult
to choose a single action based on available information, the decision is
withheld or a set of promising actions is presented to human users. The abi
lity to handle uncertain information is also required in soft decision maki
ng. In this paper. we handle decision making as a classification problem wh
ere an input pattern is classified as one of given classes. Class labels in
the classification problem correspond to alternative actions in decision m
aking. In this paper, neural networks are used as classification systems, w
hich eventually could be implemented as a part of decision making systems.
First we focus on soft decision making by trained neural networks. We assum
e that the learning of a neural network has already been completed. When a
new pattern cannot be classified as a single class with high certainty by t
he trained neural network, the classification of such a new pattern is reje
cted. After briefly describing rejection methods based on crisp outputs fro
m the trained neural network, we propose an interval-arithmetic-based rejec
tion method with interval input vectors, and extend it to the case of fuzzy
input vectors. Next we describe the learning of neural networks for possib
ility analysis. The aim of possibility analysis is to present a set of poss
ible classes of a new pattern to human users. Then we describe the learning
of neural networks from training patterns with uncertainty. Such training
patterns are denoted by interval vectors and fuzzy vectors. Finally we exam
ine the performance of various soft decision making methods described in th
is paper by computer simulations on commonly used data sets in the literatu
re. (C) 2000 Elsevier Science B.V. All rights reserved.