In multiattribute decision making a decision maker (DM) can choose the best alternative if his/her multiattribute utility function and the joint probability distribution of outcomes are exactly known. This paper develops multiattribute stochastic-statistical dominance rules which can be applied to the situation when neither of them is known exactly, that is, when the DM cannot calculate the expected utility for each alternative. First, the notion of relative risk aversion is used dominance rules are developed to screen out dominated alternatives so that hi/she choose the best one among the remaining nondominated alternatives.