Often, the real world variables are characterized with vagueness (represented by fuzzy set theory), associated hesitancy of the agent (represented by intuitionistic fuzzy set theory), and randomness (represented by probability) at the same time. Intuitionistic fuzzy set theory extends the fuzzy set theory to take account of hesitancy of the observer in addition to vagueness. We propose an integrated framework based on intuitionistic fuzzy set and probability theories to deal with the uncertainty posed by vagueness and randomness. The study is applied in an intelligent oil level controller. © 2018 IEEE.