In the decision-making by maximizing the expected utility, it is important to identify utility functions and to assess the probability distributions for each alternative. In practice, however, it appears very difficult to do this in many cases. Therefore, it becomes necessary to develop decision-supporting method on the basis of the obtainable partial knowledge of utility functions and probability distributions. One such method is by using the concept of dominance. The notions of dominance that

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... can be applied to the maximum expected utility criterion are: (a) Stochastic Dominance, by which the alternatives are ordered by comparing structure of their probability distributions under partial knowledge of utility functions, and (b) Statistical Dominance, by which the alternatives are ordered by comparing utility function values under partial knowledge of probability distributions. In this paper, stochastic dominance is first surveyed. Then, statistical dominance by Fishburn is extended, and by coupling the extended statistical dominance with stochastic dominance, Stochastic-Statistical (S-S) Dominance is developed. This dominance can be applied to the cases where only partial knowledge is available of both utility functions and probability distributions. Finally, the derived conditions for the S-S dominance are applied to an investment decision problem of stocks in Japan in order to see the feasibility of S-S dominance. By adding a reasonable criterion for incomplete knowledge of probability distributions, we can select the best alternative from among 115 alternatives on the basis of the risk aver-sion. It seems clear that S-S dominance does work as decision-supporting method under incomplete knowledge.