Interval-Based Models for Decision Problems

Abstract

Uncertainty in decision problems has been handled by probabilities with respect to unknown state of nature such as demands in market having several scenarios. Standard decision theory can not deal with non-stochastic uncertainty, indeterminacy and ignorance of the given phenomenon. Also, probability needs many data under the same situation. Recently, economical situation changes rapidly so that it is hard to collect many data under the same situation. Therefore instead of conventional ways, interval-based models for decision problems are explained as dual models in this paper. First, interval regression models are described as a kind of decision problems. Then, using interval regression model, interval weights in AHP (Analytic Hierarchy Process) can be obtained to reflect intuitive judgments given by an estimator. This approach is called interval AHP where the normality condition of interval weights is used. This normality condition can be regarded as interval probabilities. Thus, finally some basic definitions of interval probability in decision problems are shown in this paper.