Identifying efficient portfolio diversification strategies subject to stochastic dominance (SD) criteria usually assumes that the state-space of future asset returns can be captured by a fixed sample of equally probable historical returns. This paper relaxes this assumption by developing SD criteria under incomplete information on state probabilities. Specifically, we identify portfolios that dominate a given benchmark for any state probabilities in a given set. The proposed approach is applied to analyze if industrial diversification can be utilized to outperform the market portfolio. The results from this application demonstrate that the use of set-valued state probabilities can help to improve out-of-sample performance of SD-based portfolio optimization.