Fuzzy multi-stage decision-making, fuzzy state and terminal regulators and their relationship to non-fuzzy quadratic state and terminal regulators†

Bellman and Zadeh recently considered fuzzy multi-stage decision processes, the concept of fuzziness emanating from Zadeh's earlier work on fuzzy sets. Here we extend their results to processes involving continuous state and decision variables, and discuss three alternative definitions of policy membership functions, two of which were previously proposed by Bellman and Zadeh. Also discussed ( example) is the mathematical ‘ equivalence ’ between some fuzzy and non-fuzzy processes which, although profoundly different models philosophically, have the same optimal policies and optimal state realizations.