Intuitionistic fuzzy cognitive map based on fuzzy measure and integral

Fuzzy measure is a kind of set function which can represent the interaction of IF-THEN rules in reasoning, and fuzzy integral is decision tool in information fusion and process control problem. Although the fuzzy cognitive map model is an effective approach in reason process and the intuitionistic fuzzy cognitive map model introduces intuitionistic fuzzy set which uses the hesitancy as the indeterminacy degree on the inputs, it doesn´t deal with the interaction of the IF-THEN rules in the construction of an FCM. Considering the issue, we propose a new method on fuzzy cognitive map in which the fuzzy measure and fuzzy integral is the basis of the FMIFCM¿called method, and we also present the mathematical framework of the fuzzy measure, the fuzzy integral for the definition of the relative concept and the deduction of the necessary reasoning formulation. What´s more, experiment is implemented on process control problem about the industrial chemic, and the experimental results show the proposed method (FMIFCM) is effective for reasoning, compared with the traditional fuzzy cognitive map and the precious intuitionistic fuzzy cognitive map.