The computational complexity of some fuzzy dynamic programs

Fuzzy dynamic programming, a natural extension of classical dynamic programming, is of great appeal in the modeling and control of certain systems, especially those of a socio-technical systems nature. However, data acquisition, manipulation, and processing create immense problems to the systems designer interested in such realistic modeling tools. Another complication is introduced in the numerical implementation of these models. The usual dimensionality issues characteristic of conventional dynamic programming must be addressed in their fuzzy analogues. We do so for these problems via two variations of a fuzzy dynamic programming model of decision making in a fuzzy environment first proposed by Kacprzyk and then modified by Stein. We consider in particular, both time and space complexity problems associated with the model.