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.
