Abstract
A problem of decision making under uncertainty or decision making with multiple objectives is not a simple optimization problem and so we have to assume some decision principles on making a decision. So far many decision principles have been proposed as rational ones. This paper tries to reveal an underlying structure of rational decision principles. We first formulate decision problems and principles from the viewpoint of the mathematical general systems theory and then, based on them, specify the class of decision problems as a category and a decision principle as a functor. As a conclusion, we claim that three conditions, i.e., the Pareto consistency, the similarity condition and the invariance condition, compose a fundamental structure of rational decision principles and are naturally represented in the category theoretic framework. In order to support the claim we demonstrated that the linear weighted sum decision principle can be characterized by using these conditions.
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