Neural networks for soft decision making

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 di cult 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 ability to handle uncertain information is also required in soft decision making. In this paper, we handle decision making as a classi cation problem where an input pattern is classi ed as one of given classes. Class labels in the classi cation problem correspond to alternative actions in decision making. In this paper, neural networks are used as classi cation systems, which eventually could be implemented as a part of decision making systems. First we focus on soft decision making by trained neural networks. We assume that the learning of a neural network has already been completed. When a new pattern cannot be classi ed as a single class with high certainty by the trained neural network, the classi cation of such a new pattern is rejected. After brie y describing rejection methods based on crisp outputs from the trained neural network, we propose an interval-arithmetic-based rejection method with interval input vectors, and extend it to the case of fuzzy input vectors. Next we describe the learning of neural networks for possibility analysis. The aim of possibility analysis is to present a set of possible 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 examine the performance of various soft decision making methods described in this paper by computer simulations on commonly used data sets in the literature. c © 2000 Elsevier Science B.V. All rights reserved.