In this study the theory of flexibly-bounded rationality which is an extension to the theory of bounded rationality is studied. Rational decision making involves using information which is almost always imperfect and incomplete together with some intelligent machine which if it is a human being is inconsistent to make decisions. In bounded rationality, this decision is made irrespective of the fact that the information to be used is incomplete and imperfect and that the human brain is inconsistent and thus this decision that is to be made is taken within the bounds of these limitations. In the theory of flexibly-bounded rationality, advanced information analysis is used, the correlation machine is applied to complete missing information and artificial intelligence is used to make more consistent decisions. Therefore flexibly-bounded rationality expands the bounds within which rationality is exercised. Because human decision making is essentially irrational, this study proposes the theory of marginalisation of irrationality in decision making to deal with the problem of satisfying in the presence of irrationality.