Abstract
In this paper we consider multistage decision processes in Bellman and Zadeh's paper "Decision-making in a fuzzy environment" from a mathematical view-point. We propose another recursive equation which solves both stochastic and deterministic multistage decision processes in a fuzzy environment in their sense. Our result for deterministic processes coincides with their result. However, our result for stochastic processes is more or less different from theirs. Our "stochastic" recursive equation is derived through invariant imbedding. On the other hand, their "stochastic" recursive equation is a direct analogy for their deterministic one. As an example, we illustrate their numerical data, which verify the equality between simultaneous and sequential optimizations.
