Interactive multiobjective decision making under uncertainty (Q2836139)

The main merit of this book is that it presents in a unified way the state of the art in dealing with multiobjective programming problems involving uncertainty. As a general remark, the book is well written and the author, who has coauthored himself a large part of the contained results, was successful in finding an equilibrium between the mathematical rigor and the direct applicability of the algorithms by the practitioners, as the theoretical investigations and results are completed by suitable numerical examples. Worth noticing is also the fact that each chapter begins with a listing of its content, helping thus the reader to navigate more easily within the book. This almost 300-page long book is divided into seven chapters preceded by a preface and followed by the usual lists of references and most important terms. After an introduction dedicated to presenting a motivation for writing this book and to presenting the organization of its content, the second chapter presents investigations on multiobjective stochastic programming problems with both variance covariance matrices and special structures, dealt with first from a fuzzy point of view and afterwards by an interactive decision making approach. In the third chapter, multiobjective programming problems with fuzzy random variables with both variance covariance matrices and special structures are dealt with, corresponding interactive algorithms, some based on convex or linear programming, being presented in order to deliver satisfactory solutions. The next chapter discusses multiobjective multilevel stochastic programming problems, for which interactive algorithms are developed by means of different models (i.e. probability, fractile, fuzzy and random fuzzy, respectively) in order to determine satisfactory solutions, in which the hierarchical decision structure of multiple decision makers is reflected. The quite short Chapter 5 is dedicated to multiobjective two-person zero-sum games with vector and vector fuzzy payoffs, respectively. The following chapter presents instigations on generalized multiobjective programming problems with both variance covariance matrices and special structures, for which interactive algorithms based on linear and convex programming, respectively, are proposed. In the last chapter four concrete applications on farm planning and shipment are presented, showing thus, once more, the practical usability of the theoretical investigations.