Conditional decision-making in a fuzzy environment

Recently a regular (unconditional) decision process has been mathematically formulated from the multistage decision process in Bellman and Zadeh's paper ‘Decision-making in a fuzzy environment’. According to the available information on total fuzzyness, we propose two types of conditional decision process for regular decision process. One is an ‘a posteriori conditional decision process’ and the other is an ‘a priori conditional decision process’. The a posteriori process is formulated through taking at each stage backward conditional expectation of remaining process after performing take-action for the regular decision process. The a priori process is through taking at each stage backward conditional expectation before take-action. We derive recursive equations for both a posteriori and a priori processes with numerical illustrations.