Recently, many books on multiobjective programming have been published. However, only a few books have been published, in which multiobjective programming under the randomness and the fuzziness are investigated. On the other hand, several books on multilevel programming have been published, in which multiple decision makers are involved in hierarchical decision situations. In this book, we introduce the latest advances in the field of multiobjective programming and multilevel programming under uncertainty. The reader can immediately use proposed methods to solve multiobjective programming and multilevel programming, which are based on linear programming or convex programming technique. Organization of each capter is summarized as follows. In Chapter 2, multiobjective programming problems with random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 3, multiobjective programming problems with fuzzy random variables are formulated, and the corresponding interactive algorithms are developed to obtain a satisfactory solution, in which not only the uncertainty of fuzzy random variables but also the fuzziness of human's subjective judgment for permission levels are considered. In Chapter 4, multiobjective multilevel programming is discussed, and the interactive algorithms are developed to obtain a satisfactory solution, in which the hierarchical decision structure of multiple decision makers is reflected. In Chapter 5, two kinds of farm planning problems are solved by applying the proposed method, in which cost coefficients of crops are expressed by random variables.
Hitoshi Yano received his B.E. and M.E. degrees in systems engineering at Kobe University in 1980 and 1982, respectively, and his D.E. degree from Osaka University in 1988. From 1983 to 1989, he was a Research Associate in the Faculty of Economics at Kagawa University. From 1989 to 1996, he was an Associate Professor at Nagoya Municipal Women's College. From 1996 to 2004, he was an Associate Professor in the School of Humanities and Social Sciences at Nagoya City University. He is currently a Professor in the Graduate School of Humanities and Social Sciences at Nagoya City University. He won Best Paper Awards from the IAENG International Conference on Operations Research in 2011, 2013, and 2014.
