The concept of fuzziness, inspired by Zadeh (1965), brings us fruitful results when it is applied to problems in decision making. Recently, problems in fuzzy decision making are getting more complex, and one of the most complex fac� tors is dynamics in systems. Dynamical approach to fuzzy decision making has been proposed by Bellman and Zadeh's celebrated paper "Decision-making in a fuzzy environment" (1970). The idea has developed into fuzzy mathemati� cal programming and has been applied in many fields including management science, operations research, control theory, engineering, systems analysis, computer science, mathematical finance etc. Dynamic programming, advo� cated in Bellmans book "Dynamic programming" (1957), is one of the most powerful tools to deal with dynamics in systems, and Bellman and Zadeh has proposed the optimality principle in fuzzy decision making by (1970) introducing fuzzy dynamic programming. Fuzzy dynamic programming and fuzzy mathematical programming has been making remakable progress after they were given life by Bellman and Zadeh's paper (1970). In this volume, various kinds of dynamics, not only time but also structure of systems, are considered. This volume contains ten reviewed papers, which deal with dynamics in theory and applications and whose topics are poten� tially related to dynamics and are expected to develope dynamical study in near future. first, fuzzy dynamic programming is reviewed from a viewpoint of its origin and consider its developement in theory and applications.

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The book focuses on the recent dynamical development in fuzzy decision making. Various kinds of dynamics regarding not only time but also structure of systems are discussed in theory and applications. First, fuzzy dynamic programming is reviewed from a viewpoint of its origin and we consider its development in theory and applications. Next, the structure of dynamics in systems is considered in relation to fuzzy mathematical programming. Furthermore, some topics potentially related to dynamics are presented: financial management, fuzzy differential for fuzzy optimization of continuous-time fuzzy systems, and fuzzy ordering in multi-objective fuzzy systems. Finally, a unified approach in fuzzy decision making is developed. Readers can learn various kinds of methods to solve dynamical problems in fuzzy decision making through these chapters.

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