This chapter describes the theory of flexibly-bounded rationality which extends the theory of bounded rationality. Specifically, it is viewed that a decision making process which encompasses three components, information collection and analysis, the correlation, and the causal machines. Rational decision making entails utilizing information which is imperfect and incomplete jointly with human brain which is erratic on making decisions. The theory of bounded rationality prescribes making this decision despite the fact that the information is incomplete and imperfect and that the human brain is inconsistent and the decision is made within the bounds of these limitations. The theory of flexibly-bounded rationality entails using signal processing to filter noise and outliers in the data and using the correlation machine to complete missing information and artificial intelligence to make more reliable decisions. Flexibly-bounded rationality is applied to condition monitoring and HIV diagnosis problems and it is found to enlarge the bounds within which rational decision making process is employed and, thus, rises the probability of making accurate decisions than the theory of bounded rationality. 147 Causality, Correlation and Artificial Intelligence for Rational Decision Making Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/21/15. For personal use only. Causality, Correlation and Artificial Intelligence for Rational Decision Making Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/21/15. For personal use only.