Due to our increasing dependence on infrastructure networks, the attack and defense game in these networks has draw great concerns from security agencies. Moreover, when it comes to evaluating the payoffs in practical attack and defense games in infrastructure networks, the lack of consideration for the fuzziness and uncertainty of subjective human judgment brings forth significant challenges to the analysis of strategic interactions among decision makers. This paper employs intuitionistic fuzzy sets (IFSs) to depict such uncertain payoffs, and introduce a theoretical framework for analyzing the attack and defense game in infrastructure networks based on intuitionistic fuzzy theory. We take the changes in three complex network metrics as the universe of discourse, and intuitionistic fuzzy sets are employed based on this universe of discourse to reflect the satisfaction of decision makers. We employ an algorithm based on intuitionistic fuzzy theory to find the Nash equilibrium, and conduct experiments on both local and global networks. Results show that: (1) the utilization of intuitionistic fuzzy sets to depict the payoffs of attack and defense games in infrastructure networks can reflect the unique characteristics of decision makers’ subjective preferences. (2) the use of differently weighted proportions of the three complex network metrics has little impact on decision makers’ choices of different strategies.