In this article, we focus on an extended model M ¯ of bounded rationality. Based on a rationality function with lower semicontinuity, we analyze the relationship between structural stability and robustness of Ω ¯. To further demonstrate the applicability of our theory, we introduce a model Ω ¯ 0 containing an abstract rationality function and generalize abstract fuzzy economies. We demonstrate the structural stability of the extended model Ω ¯ 0 at ξ ¯, ɛ. That is to say, Ω ¯ (...) 0 is robust to the ξ ¯, ɛ -equilibria. (shrink)