The 6th International Conference on Modeling Decisions for Artificial Intelligence (MDAI) was held at Awaji Island, Japan, from November 30 to December 2, 2009 and was the inspiration for this special issue. The nine selected papers concern soft computing tool applications. The first, by Yoshida, studies the risk analysis of portfolios under uncertainty and gives expressions showing explicit relationships among parameters in a portfolio. The second, by Entani, proposes an efficiency-interval-based measure based on interval data envelopment analysis. The third, by Hamasuna, Endo, and Miyamoto, concerns clustering for data with tolerance and proposes algorithms for this type of data. The fourth, by Endo, Hasegawa, Hamasuna, and Kanzawa, focuses on fuzzy c-means clustering for uncertain data using quadratic regularization. The fifth, by Honda, Notsu, and Ichihashi, also involves clustering, focusing on variable selection/weighting in PCA-guided k-means. The sixth, by Hwang and Miyamoto, covers clustering focusing on kernel fuzzy c-means and some interesting new results. The seventh, by Kanzawa, Endo, and Miyamoto, uses fuzzy c-means in semisupervised fuzzy c-means. The eighth, by Kudo and Murai, is devoted to rough sets, proposing a heuristic algorithm for calculating a relative reduct candidate. The closing contribution, by Kusunoki and Inuiguchi, is also devoted to rough sets, with the authors studying rough set models in information tables with missing values. We thank the referees for their review work, and the Fuji Technology Press Ltd. staff for its encouragement and advice.
