| Summary: | Fuzzy cognitive map has gradually emerged as a powerful paradigm for uncertain knowledge representation and a simulation mechanism that is applicable in dealing with complex artificial reasoning problems. To better model uncertain inference reasoning problems, we propose an extended intuitionistic fuzzy cognitive map via Dempster-Shafer theory. First of all, some new operations on IFSs are introduced from the perspective of Dempster-Shafer theory. Then, the extended intuitionistic fuzzy cognitive map is established via the proposed new operations. Next, we investigate the problem of modeling complex system from multiple decision makers using extended intuitionistic fuzzy cognitive maps and present a method to aggregate a number of maps. Particular emphases are put on defining the augmented connection matrices, determining the importance levels of different extended intuitionistic fuzzy cognitive maps and aggregating them. Finally, the performances of extended intuitionistic fuzzy cognitive maps have been validated through a number of simulations. The simulations indicate that the theory of extended intuitionistic fuzzy cognitive map not only provides much more choices to model complex system but also reduces the computational complexity by comparison with intuitionistic fuzzy cognitive map.
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