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The application of dynamic programming to the modeling of decision control problems arising in research and development systems management is discussed. Probabilistic models for treating an allocation problem in the context of an antiballistic missile system are first reviewed in order to set the background for the use of fuzzy sets. Fuzzy research and development (R&D) systems are exemplified in the context of allocation problems occurring in cancer research appropriation. By recourse to fuzzy set theory, fuzzy dynamic programming models with their corresponding flow charts are then developed for an allocation problem arising in R&D systems. It is argued that the use of fuzzy set theory will generally provide models of better proximity to the systems modeled than the traditional deterministic and stochastic approaches. The computational problems in fuzzy algorithms are discussed. A method for deriving the membership function values is also presented. An example of the use of the digital computer to derive computational results from the models is presented.